Articles

Document Type

Journal article (JA)

Title

Global classical solutions of compressible isentropic Navier–Stokes equations with small density

Author

Si, Xin(1); Zhang, Jianwen(2); Zhao, Junning(2)

Address

(1) School of Applied Mathematics, Xiamen University of Technology, Xiamen; 361024, China; (2) School of Mathematical Sciences, Xiamen University, Xiamen; 361005, China

RPAddress


Email


ResearchID


ORCID


Journal

Nonlinear Analysis: Real World Applications

Publisher

Elsevier Ltd

ISSN

14681218

Published

201808, 42:5370.

JCR

1

ImpactFactor

1.659

ISBN


Fund_Code


HYMC


HYDD


HYKSRQ


HYJSRQ


HYLWLB


HYJB


Keywords

Nonlinear equations  Partial differential equations  Vacuum

Abstract

This paper concerns the Cauchy problem of compressible isentropic Navier–Stokes equations in the whole space R3. First, we show that if ρ0∈Lγ∩H3, then the problem has a unique global classical solution on R3×[0,T] with any T∈(0,∞), provided the upper bound of the initial density is suitably small and the adiabatic exponent γ∈(1,6). If, in addition, the conservation law of the total mass is satisfied (i.e., ρ0∈L1), then the global existence theorem with small density holds for any γ>1. It is worth mentioning that the initial total energy can be arbitrarily large and the initial vacuum is allowed. Thus, the results obtained particularly extend the one due to Huang–Li–Xin (Huang et al., 2012), where the global wellposedness of classical solutions with small energy was proved. ? 2017 Elsevier Ltd

WOS Categories


Accession Number


EI收录号

20180204629722

DOI

10.1016/j.nonrwa.2017.12.005

ESI_Type

MATHEMATICS

Collection

EI

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