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References (43)
-
Shuji Machihara, T. Ozawa (2002)
Interpolation inequalities in Besov spaces, 131
-
(1960)
Studies onmagneto - hydrodynamicwaves and other anisotropicwavemotions -
Jishan Fan, B. Ahmad, T. Hayat, Yong Zhou (2016)
On well-posedness and blow-up for the full compressible Hall-MHD systemNonlinear Analysis-real World Applications, 31
-
Jishan Fan, Xuanji Jia, G. Nakamura, Yong Zhou (2015)
On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effectsZeitschrift für angewandte Mathematik und Physik, 66
-
H Triebel (1983)
10.1007/978-3-0346-0416-1Theory of Function Spaces, Monographs in Mathematics
-
R Coifman (1993)
247J. Math. Pures. Appl., 72
-
Y Wang, H Li (2016)
Beale–Kato–Majda criteria of smooth solutions to the 3D Hall-MHD flowsAppl. Math. Comput., 286
-
H. Kozono, Y. Taniuchi (2000)
Bilinear estimates in BMO and the Navier-Stokes equationsMathematische Zeitschrift, 235
-
Renhui Wan, Yong Zhou (2015)
On global existence, energy decay and blow-up criteria for the Hall-MHD systemJournal of Differential Equations, 259
-
MJ Lighthill (1960)
397Philos. Trans. R. Soc. Lond. Ser. A, 252
-
J Fan (2017)
2438Comput. Math. Appl., 74
-
Renhui Wan, Yong Zhou (2019)
Global Well-Posedness for the 3D Incompressible Hall-Magnetohydrodynamic Equations with Fujita–Kato Type Initial DataJournal of Mathematical Fluid Mechanics, 21
-
B. Somov (2010)
Magnetic reconnection in solar flaresPhysics-Uspekhi, 53
-
M Acheritogaray (2011)
901Kinet. Relat. Models, 4
-
Fangyi He, B. Ahmad, T. Hayat, Yong Zhou (2016)
On regularity criteria for the 3D Hall-MHD equations in terms of the velocityNonlinear Analysis-real World Applications, 32
-
D. Chae, Renhui Wan, Jiahong Wu (2014)
Local Well-Posedness for the Hall-MHD Equations with Fractional Magnetic DiffusionJournal of Mathematical Fluid Mechanics, 17
-
Zhen Lei, Yi Zhou (2009)
BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero ViscosityarXiv: Analysis of PDEs
-
Mimi Dai (2015)
Regularity criterion for the 3D Hall-magneto-hydrodynamicsarXiv: Analysis of PDEs
-
Weijiang Gu, Caochuan Ma, Jianzhu Sun (2016)
A regularity criterion for the generalized Hall-MHD systemBoundary Value Problems, 2016
-
J Fan (2015)
1156Z. Angew. Math. Mech., 95
-
S Gala (2007)
339Serdica Math. J., 33
-
Renhui Wan, Yong Zhou (2019)
Global well-posedness, BKM blow-up criteria and zero h limit for the 3D incompressible Hall-MHD equationsJournal of Differential Equations
-
D. Chae, P. Degond, Jian‐Guo Liu (2012)
Well-posedness for Hall-magnetohydrodynamicsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 31
-
Zujin Zhang (2016)
A remark on the blow-up criterion for the 3D Hall-MHD system in Besov spacesJournal of Mathematical Analysis and Applications, 441
-
D. Chae, J. Wolf (2015)
On Partial Regularity for the 3D Nonstationary Hall Magnetohydrodynamics Equations on the PlaneSIAM J. Math. Anal., 48
-
Renhui Wan, Yong Zhou (2017)
Low Regularity Well-Posedness for the 3D Generalized Hall-MHD SystemActa Applicandae Mathematicae, 147
-
J. Beale, Tosio Kato, A. Majda (1984)
Remarks on the breakdown of smooth solutions for the 3-D Euler equationsCommunications in Mathematical Physics, 94
-
H. Kozono, T. Ogawa, Y. Taniuchi (2002)
The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equationsMathematische Zeitschrift, 242
-
D. Chae, Jihoon Lee (2013)
On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamicsJournal of Differential Equations, 256
-
A. Alghamdi, S. Gala, M. Ragusa (2018)
New regularity criteria for the 3D Hall-MHD equationsAnnales Polonici Mathematici, 121
-
Tosio Kato, G. Ponce (1988)
Commutator estimates and the euler and navier‐stokes equationsCommunications on Pure and Applied Mathematics, 41
-
D. Chae, J. Wolf (2015)
On Partial Regularity for the Steady Hall Magnetohydrodynamics SystemCommunications in Mathematical Physics, 339
-
TG Forbes (1991)
15Geophys. Astrophys. Fluid Dyn., 62
-
Yuzhu Wang, Weibing Zuo (2013)
On the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosityCommunications on Pure and Applied Analysis, 13
-
Jishan Fan, A. Alsaedi, T. Hayat, G. Nakamura, Yong Zhou (2015)
On strong solutions to the compressible Hall-magnetohydrodynamic systemNonlinear Analysis-real World Applications, 22
-
A. Alghamdi, S. Gala, M. Ragusa (2018)
A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations, 3
-
D. Chae, M. Schonbek (2013)
On the temporal decay for the Hall-magnetohydrodynamic equationsJournal of Differential Equations, 255
-
S. Gala (2007)
A Note on Div-Curl LemmaSerdica. Mathematical Journal, 33
-
D. Chae, S. Weng (2013)
Singularity formation for the incompressible Hall-MHD equations without resistivityarXiv: Analysis of PDEs
-
J. Polygiannakis, X. Moussas (2001)
A review of magneto-vorticity induction in Hall-MHD plasmasPlasma Physics and Controlled Fusion, 43
-
R. Coifman, P. Lions, Y. Meyer, S. Semmes (1993)
Compensated compactness and Hardy spacesJournal de Mathématiques Pures et Appliquées, 72
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
S Gala (2016)
18. 10Z. Angew. Math. Phys., 67
- Publisher
- Springer Journals
- Copyright
- Copyright © Sociedade Brasileira de Matemática 2021
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-021-00256-7
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we investigate the Cauchy problem for the 3D incompressible Hall-MHD equations with zero viscosity. We prove the Beale–Kato–Majda regularity criterion of smooth solutions in terms of the velocity field and magnetic field in the homogeneous Besov spaces B˙∞,∞0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\dot{B}}_{\infty ,\infty }^{0} $$\end{document}. Then we give a criterion on extension beyond T of our local solution. Our result may be also regarded as an extension of the corresponding result of Wang and Zuo (Commun Pure Appl Anal 13:1327–1336, 2014).
Journal
"Bulletin of the Brazilian Mathematical Society, New Series" – Springer Journals
Published: Mar 1, 2022
Keywords: Hall-magnetohydrodynamic equations; Smooth solutions; Besov space, blow up criterion; 35B65; 76W05