Access the full text.
Sign up today, get DeepDyve free for 14 days.
Matthias Hess, Matthias Hieber, A. Mahalov, J. Saal (2010)
Nonlinear stability of Ekman boundary layersBulletin of the London Mathematical Society, 42
Matthias Hieber, Huanyao Wen, Ruizhao Zi (2019)
Optimal decay rates for solutions to the incompressible Oldroyd-B model in R3Nonlinearity, 32
(1994)
Spectral theory and Cauchy problems on L p spaces
(2013)
Global existence results for Oldroyd-B fluids on exterior domains with non small coupling parameters
Matthias Hieber (1991)
Integrated semigroups and differential operators onLp spacesMathematische Annalen, 291
(1997)
Heat kernels and maximal L p-Lq -estimates for solutions of parabolic evolution equations
Matthias Hieber, W. Stannat (2013)
Stochastic stability of the Ekman spiralAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 12
Matthias Hieber, James Robinson, Y. Shibata (2020)
Mathematical Analysis of the Navier-Stokes Equations
(2018)
Modeling and analysis of Ericksen-Leslie equations for nematic liquid crystal flow
(2013)
L p - theory of fluid - rigid body interactions for Newtonian and generalized Non - Newtonian fluids
D. Bothe, R. Denk, Matthias Hieber, R. Schnaubelt, Gieri Simonett, M. Wilke, Rico Zacher (2017)
PrefaceJournal of Evolution Equations, 17
(2000)
Heat-Kernels and maximal regularity: the non-autonomous case
(2008)
Functional Analysis and Evolution Equations: The Günter Lumer Volume, Birkhäuser, xvii + 636pp
R. Denk, Matthias Hieber, F. Bertola, C. Kharif (2003)
Fourier multipliers and problems of elliptic and parabolic type
(2001)
Prüss), L p -Theory of the Stokes operator in a half space
Hermann, Kellerman, Matthias Hieber, Mathematisches (2003)
Integrated Semigroups
Matthias Hieber, J. Prüss (2019)
Dynamics of the Ericksen–Leslie Equations with General Leslie Stress II: The Compressible Isotropic CaseArchive for Rational Mechanics and Analysis, 233
Matthias Hieber, J. Prüss (2019)
Bounded H ∞ -calculus for a class of nonlocal operators: the bidomain operator in the L q -setting
Matthias Hieber (2010)
IP SPECTRA OF PSEUDODIFFERENTIAL OPERATORS GENERATING INTEGRATED SEMIGROUPS
M. Geissert, Horst Heck, Matthias Hieber (2006)
On the Equation div u = g and Bogovskii’s Operator in Sobolev Spaces of Negative Order, 168
M. Geissert, Matthias Hieber, Thieu Nguyen (2016)
A General Approach to Time Periodic Incompressible Viscous Fluid Flow ProblemsArchive for Rational Mechanics and Analysis, 220
Matthias Hieber, P. Maremonti (2016)
Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions
Ken Furukawa, Y. Giga, Matthias Hieber, Amru Hussein, Takahito Kashiwabara, M. Wrona (2018)
Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equationsNonlinearity, 33
Matthias Hieber, J. Prüss (1998)
Functional calculi for linear operators in vector-valued $L^p$-spaces via the transference principleAdvances in Differential Equations
Matthias Hieber, J. Prüss (2016)
Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic caseMathematische Annalen, 369
Matthias Hieber, Takahito Kashiwabara (2015)
Global Strong Well-Posedness of the Three Dimensional Primitive Equations in $${L^p}$$Lp-SpacesArchive for Rational Mechanics and Analysis, 221
K. Abe, Y. Giga, Matthias Hieber (2012)
Stokes Resolvent Estimates in Spaces of Bounded FunctionsAnnales Scientifiques De L Ecole Normale Superieure, 48
(2010)
The Fujita-Kato approach to the equations of Navier-Stokes in the rotational setting
(2006)
p-theory of the Navier-Stokes flow in the exterior of a rotating or moving domain
Matthias Hieber, O. Sawada (2005)
The Navier-Stokes Equations in ℝn with Linearly Growing Initial DataArchive for Rational Mechanics and Analysis, 175
Matthias Hieber (1996)
Gaussian Estimates and Holomorphy of Semigroups on Lp SpacesJournal of The London Mathematical Society-second Series, 54
Matthias Hieber, Manuel Nesensohn, J. Prǔss, K. Schade (2013)
Dynamics of Nematic Liquid Crystal Flows: the Quasilinear ApproacharXiv: Analysis of PDEs
James Robinson (2020)
Partial Regularity for the 3D Navier–Stokes Equations
M. Geissert, Horst Heck, Matthias Hieber, O. Sawada (2011)
Weak Neumann implies Stokes, 2012
Matthias Hieber (2019)
A Characterization of the Growth Bound of a Semigroup via Fourier MultipliersEvolution Equations and Their Applications in Physical and Life Sciences
(2006)
p-Lq estimates for parabolic systems with V MO-coefficients
G. Galdi, Matthias Hieber, Takahito Kashiwabara (2015)
Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forcesNonlinearity, 30
Matthias Hieber, J. Prüss (2018)
On the bidomain problem with FitzHugh–Nagumo transportArchiv der Mathematik, 111
(2011)
Zajaczkowski), Preface. Parabolic Problems
(1994)
Simonett), Bounded H ∞ -calculus for elliptic operators
Julia, Montel. (2011)
Vector-valued Laplace Transforms and Cauchy Problems
(2020)
The hydrostatic Stokes operator and wellposedness of the primitive equations on spaces of bounded functions
(2007)
Optimal L p − L q estimates for parabolic boundary value problems with inhomogeneous boundary data
Matthias Hieber, H. Kozono, Anton Seyfert, Senjo Shimizu, T. Yanagisawa (2020)
The Helmholtz–Weyl decomposition of $$L^r$$ L r vector fields for two dimensional exterior domainsThe Journal of Geometric Analysis, 31
Matthias Hieber, J. Saal (2018)
The stokes equation in the Lp-setting: Well-posedness and regularity properties
J. Evol. Equ. 21 (2021), 2779–2786 © 2021 The Author(s) Journal of Evolution 1424-3199/21/032779-8, published online November 26, 2021 Equations https://doi.org/10.1007/s00028-021-00751-w Robert Denk, Yoshikazu Giga, Hideo Kozono, Jürgen Saal, Gieri Simonett and Edriss Titi Matthias Hieber, June 2020 Matthias Hieber studied Mathematics and Physics at the Universities of Tübingen, Besançon and Tulane in the early 1980s. In 1989, he received his doctoral degree in Mathematics under the supervision of Wolfgang Arendt and Helmut H. Schaefer from the University of Tübingen. Matthias Hieber’s Ph.D. thesis was on integrated semigroups and differential operators on L . On the one side, he set sights on Banach space-valued Laplace transforms and spectral theory [1,4,5] and on the other side on functional analytic tools for partial differential equations, like the Schrödinger equation [2]. A highlight is this direction is the monograph “Vector Valued Laplace Transforms and Cauchy Problems” [B1], published jointly with Wolfgang Arendt, Charles Batty and Frank Neubrander in the Birkhäuser Monographs Series. From 1990 to 1995, he held a position as Oberassistent at the University of Zurich. There, his research interests shifted more and more toward properties of elliptic oper- ators arising in partial differential equations of evolution type. His publications during this period demonstrate the significance of heat kernel and Gaussian estimates as well of the H -calculus in the treatment of evolution systems [3,6,8,9]. In 1995, he com- pleted his habilitation under the mentorship of Herbert Amann at the University of Zurich. He then held positions as Professeur Associé at the Université de Franche-Comté at Besançon and as Hochschuldozent at the Karlsruhe Institute of Technology. During his years in Besançon and Karlsruhe, great advances in the theory of maximal reg- ularity were made. From the beginning, Matthias was significantly involved in this 2780 R. Denk et al. J. Evol. Equ. development, resulting in the influential results [7,9] that sectorial operators on L - spaces satisfying a heat kernel bound (or more generally a Poisson bound) admit the property of maximal L -regularity or on functional calculi for operators on vector- valued L -spaces via the transference principle [8]. In 1999, he was appointed full professor at the Technische Universität Darmstadt and he became head of the Applied Analysis Group there. He continued to work on maximal regularity properties of evolution equations. In fact, his joint publications [12,17,B2] with Robert Denk, Giovanni Dore, Jan Prüss and Alberto Venni on para- bolic systems were quite influential and became highly cited sources for the theory of maximal regularity, H -calculus and its applications to partial differential equations. Extensions to L − L -estimates for parabolic systems with only VMO-coefficients p q were obtained jointly with Horst Heck and Robert Haller in [16]. A new characteri- zation of the growth bound of a semigroup based on Fourier multiplier methods was given by him in [10]. At the same time, his research interests started to shift to the field of mathematical fluid dynamics. In [11], jointly with Jan Prüss and Wolfgang Desch, he investigated the Stokes operator in a half space and proved the surprising result that the Stokes ∞ n operator generates an analytic semigroup on the solenoidal subspace of L (R ),but 1 n not on L (R ). Further results concerned the Navier–Stokes equations with linearly growing data ( [13] jointly with Okihiro Sawada) or in the exterior of moving domains ([14] jointly with Matthias Geissert and Horst Heck). During the first decade in Darmstadt, his research group grew continuously, in spite of the fact that he was occupied as Dean of the Department of Mathematics. In subsequent years, Matthias played a leading role in various collaborative research initiatives. From 2007 to 2014, he was Principal Investigator and member of the Steering Committee of the Center of Excellence “Smart Interfaces” at TU Darmstadt (EXC259). From 2009 to 2018, he was the Spokesperson of the “International Research Training Group (IRTG1529)” on Mathematical Fluid Dynamics, a joint cooperation between TU Darmstadt, Waseda University and The University of Tokyo, funded by DFG and JSPS. On the Japanese side, this program was coordinated by Yoshihiro Shibata and Hideo Kozono. The rich scientific outcome of these research initiatives, especially of the IRTG, con- tributed to a deeper understanding of fluid dynamical phenomena and related topics. Let us mention here results on Bogovskii’s operator in Sobolev spaces of negative or- der [15], fluid structure interaction problems [21], complex fluids as described, e.g., by Oldroyd-B models [23,34], as well as on the Navier–Stokes equations in the rotational setting [18]. A special focus lied on the theory of the Stokes equation: Remarkable results jointly with Ken Abe, Yoshikazu Giga and Paolo Maremonti show that the Stokes operator generates an analytic semigroup on the solenoidal subspace of L () [24,25] for cer- tain classes of domains ⊂ R . Further results connect the weak Neumann problem to the Navier–Stokes equations [20]; we refer also the survey article [32] jointly with Jürgen Saal. Vol. 21 (2021) Preface 2781 Another focal point was the analysis and modeling of nematic liquid crystal flows. A new thermodynamically consistent understanding of these flows established in collaboration with Jan Prüss in [31] paved the way for a thorough understanding of the general Ericksen–Leslie model subject to general Leslie stress by means of the theory of quasilinear evolution equations. The beautiful articles [26,30,31,35] present far reaching local and small data global existence results for strong solutions for this system in the compressible and incompressible situation. For the first time, no struc- tural conditions on the Leslie coefficients, as, e.g., Parodi’s relation, were needed for the analysis of the general Ericksen–Leslie system. Matthias also obtained important results on periodic solutions for incompressible fluid flow problems. A general framework was developed in [27], and the situation of arbitrarily large forces in the context of the primitive equations is described in [29]in joint work with Paolo Galdi and Takahito Kashiwabara. In the last years, he was particularly interested in geophysical flows and the primitive equations. A fundamentally new approach to the latter equations was developed jointly with Takahito Kashiwabara in [28]. The situation of bounded data and its relationship to the uniqueness problem for weak solutions was analyzed in a German–Japanese team including Yoshikazu Giga in the articles [36,37]. The stability of Ekman layers arising in geophysical flows was described in the deterministic and stochastic setting in [19] and [22]. His broad range of interests is also documented by recent regularity and global existence results for nonlocal equations, like the bidomain equations [33,38], jointly with Jan Prüss, and through new contributions in geometric analysis concerning the Helmholtz–Weyl decomposition of L -vector fields in exterior domains [39], jointly with Hideo Kozono, Senjo Shimizu and others. Over the years, Matthias Hieber received several offers from renowned German Universities; however, he decided to stay at TU Darmstadt. He held visiting professor or visiting scholar positions at highly ranked mathematical institutes all over the world, among them the University of California at Berkeley, UCLA, the Courant Institute and the University of Tokyo. In addition, he received several honorable distinctions: Since 2012, he is adjunct professor at the University of Pittsburgh; from 2016 to 2019, he was guest professor at Waseda University in Tokyo. Since 2020, he serves as the Vice-Director of the Mathematical Research Institute in Oberwolfach. As a trend-setting mathematician, Matthias made numerous important contributions to the analytical understanding of evolution equations. He published more than one hundred research papers, co-authored three monographs [B1,B2,B5], three special volumes [V1,V2,V3] and wrote two textbooks [B3,B4]. His mathematical expertise comprises the development of evolution equations and also its application to concrete problems arising in the applied sciences. For his Ph.D. students, he has been a steady source of motivation and encouragement. One reason for attracting about twenty Ph.D. students, up to now, lies in his ability to share and to transfer his enthusiasm for mathematical research. Like this, he was very pleased to host Okihiro Sawada and Huy Nguyen as Humboldt Research Fellows as well as 2782 R. Denk et al. J. Evol. Equ. numerous scholars in Darmstadt. He also acted as a mentor for five habilitations at TU Darmstadt. We also would like to mention here the organization of several workshops at Ober- wolfach on Geophysical Flows, jointly with Yoshikazu Giga and Edriss Titi. He also serves as a member of the editorial boards of various journals including “Differential and Integral Equations,” “Advances in Differential Equations” and “Journal of Mathe- matical Fluid Mechanics” as well as for the “Springer Lectures Notes in Mathematical Fluid Dynamics.” His scientific achievements, his broad interests, his contagious enthusiasm for math- ematics, his sense of humor and his communication skills all contribute to the high standing Matthias Hieber enjoys in the mathematical community. It is, then, not sur- prising that he was invited to numerous summerschools as a lecturer. The collection of original research papers in this volume reflects the wide-ranging scientific interests of Matthias Hieber. It is inspired by the Conference “Evolution Equations: Applied and Abstract Perspectives,” held on October 28–November 1, 2019, at CIRM in Luminy, France, on the occasion of his 60th birthday, and which was organized by Karoline Disser, Robert Haller-Dintelmann, Horst Heck, Mads Kyed, Jürgen Saal, Okihiro Sawada and Ian Wood. We express our gratitude to the organizers and participants of the conference and, of course, to all contributors of this volume. Finally, we would like to thank Wolfgang Arendt and Michel Pierre, the Editors-in- Chief of Journal of Evolution Equations, as well as Jan Holland from Springer Verlag, for their help and continuous support in publishing this special volume. Funding Open Access funding enabled and organized by Projekt DEAL. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/ by/4.0/. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Monographs and Textbooks [B1] (with W. Arendt, Ch. Batty, F. Neubrander), Vector Valued Laplace Transforms and Cauchy Prob- lems. Monographs in Mathematics, 96, xi + 523pp., Birkhäuser, 2001. Second Edition, 2011. [B2] (with R. Denk, J. Prüss), R-Boundedness, Fourier Multipliers and Problems of Elliptic and Para- bolic Type. Memoirs Amer. Math. Soc., vii + 114pp., 2003. [B3] Analysis I. Springer Spektrum, x + 291pp., 2018. [B4] Analysis II. Springer Spektrum, x+ 203pp., 2019. Vol. 21 (2021) Preface 2783 [B5] (with J. Robinson, Y. Shibata), Mathematical Analysis of the Navier-Stokes Equations. Lecture Notes in Math., Vol. 2254, Springer, 2020. Special Volumes and Festschriften [V1] (with H. Amann, W. Arendt, F. Neubrander, S. Nicaise, J. von Below), Functional Analysis and Evolution Equations: The Günter Lumer Volume, Birkhäuser, xvii + 636pp., 2008. [V2] (with J. Escher, P. Guidotti, P. Mucha, J. Prüss, Y. Shibata, G. Simonett, C. Walker, W. Za- jaczkowski), Preface. Parabolic Problems, Prog. Nonlinear Differential Equations Appl. 80, Birkhäuser, ix-xii, 2011. [V3] (with D. Bothe, R. Denk, R. Schnaubelt, G. Simonett, M. Wilke, R. Zacher), Special issue: Parabolic evolution equations, maximal regularity, and applications–dedicated to Jan Prüss. J. Evol. Equ., 17, (2017). Selected Articles [1] (with H. Kellermann), Integrated semigroups. J. Funct. Anal., 84 (1989), 160-180. [2] Integrated semigroups and differential operators on L spaces. Math. Ann., 291 (1991), 1-16. [3] (with H. Amann, G. Simonett), Bounded H -calculus for elliptic operators. Diff. Integral Equa- tions, 7 (1994), 613-653. [4] Spectral theory and Cauchy problems on L spaces. Math. Z., 216 (1994), 613-628. [5] L spectra of pseudodifferential operators generating integrated semigroups. Trans. Amer. Math. Soc., 347 (1995), 4023-4035. [6] Gaussian estimates and holomorphy of semigroups on L spaces. J. London Math. Soc., 54 (1996), 148-160. p q [7] (with J. Prüss), Heat kernels and maximal L -L -estimates for solutions of parabolic evolution equations. Comm. Partial Differential Equations, 22 (1997), 1647-1669. [8] (with J. Prüss), Functional calculi for linear operators in vector-valued L -spaces via the transfer- ence principle. Adv. Diff. Equations, 3 (1998), 847-872. [9] (with S. Monniaux), Heat-Kernels and maximal regularity: the non-autonomous case. J. Fourier Anal. Appl., 6 (2000), 467-481. [10] A Characterization of the growth bound of a semigroup via Fourier multipliers. In: Evolution Equations and Their Applications, G. Lumer, L. Weis (eds.), Marcel Dekker, (2001), 121-124. [11] (with W. Desch, J. Prüss), L -Theory of the Stokes operator in a half space. J. Evol. Equ., 1 (2001), 115-142. [12] (with R. Denk, G. Dore, J. Prüss, A. Venni), New thoughts on old ideas of R.T. Seeley. Math. Ann., 328 (2004), 545-583. [13] (with O. Sawada), The Navier-Stokes equations in R with linearly growing initial data. Arch. Rational Mech. Anal., 175 (2005), 269-285. [14] (with M. Geissert, H. Heck), L -theory of the Navier-Stokes flow in the exterior of a rotating or moving domain. J. reine angew. Math., 596 (2006), 45-62. [15] (with M. Geissert, H. Heck), On the equation di v u = g and Bogovskii’s operator in Sobolev spaces of negative order Operator Theory, 168 (2006), 113-121. p q [16] (with R. Haller, H. Heck), L -L estimates for parabolic systems with VMO-coefficients. J. London Math. Soc., 74 (2006), 717-736. p q [17] (with R. Denk, J. Prüss), Optimal L − L estimates for parabolic boundary value problems with inhomogeneous boundary data. Math. Z., 257 (2007), 193-224. [18] (with Y. Shibata), The Fujita-Kato approach to the equations of Navier-Stokes in the rotational setting. Math. Z., 265, (2010) 481-493. [19] (with M. Hess, A. Mahalov, J. Saal), Nonlinear stability of Ekman boundary layers. Bull. London Math. Soc., 42, (2010), 691-706. [20] (with M. Geissert, H. Heck, O. Sawada), Weak Neumann implies Stokes. J. Reine Angew. Math., 669, (2012), 75-100. 2784 R. Denk et al. J. Evol. Equ. [21] (with K. Götze, M. Geissert), L -theory of fluid-rigid body interactions for Newtonian and gener- alized Non-Newtonian fluids. Trans. Amer. Math. Soc., 365 (2013), 1393-1439. [22] (with W. Stannat), Stochastic stability of the Ekman spiral, Ann. Sc. Norm. Super Pisa, 12, (2013), 189-208. [23] (with D. Fang, R. Zi), Global existence results for Oldroyd-B fluids on exterior domains with non small coupling parameters. Math. Ann., 356 (2013), 687-709. [24] (with K. Abe, Y. Giga), Stokes resolvent estimates in spaces of bounded functions. Ann. Sci. Ec. Norm. Super., 48 (2015), 537-559. [25] (with P. Maremonti), Bounded analyticity of the Stokes semigroup on spaces of bounded functions. In: Recent Develpments in MFD. H. Amann, Y. Giga, H. Kozono, H. Okamoto (eds.), Birkhauser, 2015, 275-289. [26] (with M. Nesensohn, J. Pruess, K. Schade), Dynamics of nematic liquid crystal flow: the quasilinear approach. Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (2016), 397-408. [27] (with M. Geissert, H. Nguyen), A general approach to time periodic incompressible viscous fluid flow problems. Arch. Rational Mech. Anal., 220, (2016), 1095-1118. [28] (with T. Kashiwabara), Global strong well-posedness of the three dimensional primitive equations in L -spaces. Arch. Rational Mech. Anal., 221, (2016), 1077-1115. [29] (with G.P. Galdi, T. Kashiwabara), Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces. Nonlinearity, 30, (2017), 3979-3992. [30] (with J. Prüss), Dynamics of the Ericksen-Leslie equations with general Leslie stress I: the incom- pressible isotropic case. Math. Ann., 369, (2017), 977-996. [31] (with J. Prüss), Modeling and analysis of Ericksen-Leslie equations for nematic liquid crystal flow. In: Handbook of Math. Anal. in Mechanics of Viscous Fluids, Y. Giga, A. Novotny (eds.), Vol.2, Springer, 2018, 1057-1134. [32] (with J. Saal), The Stokes equation in the L -setting: well-posedness and regularity properties, In: Handbook of Math. Anal. in Mechanics of Viscous Fluids, Y. Giga, A. Novotny (eds.), Vol.1, Springer, 2018, 117-206. [33] (with J. Prüss), On the bidomain problem with Fitzhugh-Nagumo transport. Archiv Math., 111, (2018), 313-327. [34] (with H. Wen, R. Zi), Optimal decay rates for solutions to the incompressible Oldroyd-B model in R . Nonlinearity, 32, (2019), 833-852. [35] (with J. Prüss), Dynamics of Ericksen-Leslie equations with general Leslie stress II: The compress- ible isotropic case. Arch. Rational Mech. Anal., 233, (2019), 1441-1468. [36] (with K. Furukawa, Y. Giga, A. Hussein, T. Kashiwabara, M. Wrona), Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations. Nonlin- earity, 33 (2020), 6502-6516. [37] (with Y. Giga, M. Gries, A. Hussein, T. Kashiwabara), The hydrostatic Stokes operator and well- posedness of the primitive equations on spaces of bounded functions. J. Funct. Anal., 279, (2020), [38] (with J. Prüss), Bounded H -calculus for a class of nonlocal operators: the bidomain operator in the L -setting. Math. Ann., 378, (2020), 6502-6516. [39] (with H. Kozono, A. Seyfert, S. Shimizu, T. Yanagisawa), The Helmholtz-Weyl decomposition of L -vector fields for two dimensional exterior domains. J. Geom. Anal., 31, (2021), 5146-5165. Robert Denk Fachbereich Mathematik und Statistik Universität Konstanz 78457 Konstanz Germany E-mail: robert.denk@uni-konstanz.de Vol. 21 (2021) Preface 2785 Yoshikazu Giga Graduate School of Mathematical Sciences The University of Tokyo Komaba 3-8-1 Meguro Tokyo 153-8914 Japan E-mail: ygiga@ms.u-tokyo.ac.jp Hideo Kozono Department of Mathematics Waseda University Tokyo 169-8555 Japan E-mail: kozono@waseda.jp ; hideo.kozono.c7@tohoku.ac.jp and Research Alliance Center of Mathematical Sciences Tohoku University 980-8578 Sendai Japan Jürgen Saal Heinrich-Heine-Universität Düsseldorf Mathematisches Institut 40204 Düsseldorf Germany E-mail: juergen.saal@hhu.de Gieri Simonett Department of Mathematics Vanderbilt University Nashville TN 37240 USA E-mail: gieri.simonett@vanderbilt.edu Edriss Titi Department of Mathematics Texas A&M University College Station TX 77843 USA E-mail: titi@math.tamu.edu ; edriss.titi@damtp.cam.ac.uk and Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA UK 2786 R. Denk et al. J. Evol. Equ. and Department of Computer Science and Applied Math- ematics Weizmann Institute of Science Rehovot 7610001 Israel
Journal of Evolution Equations – Springer Journals
Published: Sep 1, 2021
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.