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
1468-1218
Published
2018-08, 42:53-70.
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 well-posedness 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

Back to List