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Global strong solutions of the Cauchy problem for 1D compressible Navier-Stokes equations with density-dependent viscosity

Global strong solutions of the Cauchy problem for 1D compressible Navier-Stokes equations with... We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ(ρ) = Aρ α , where α > 0 and A > 0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Global strong solutions of the Cauchy problem for 1D compressible Navier-Stokes equations with density-dependent viscosity

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-016-0631-4
Publisher site
See Article on Publisher Site

Abstract

We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ(ρ) = Aρ α , where α > 0 and A > 0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 15, 2017

References