NDLI: Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier

Content Provider	Springer Nature Link
Author	Fang, Li Guo, Zhenhua
Copyright Year	2016
Abstract	The aim of this paper is to establish the global well-posedness and large-time asymptotic behavior of the strong solution to the Cauchy problem of the two-dimensional compressible Navier–Stokes equations with vacuum. It is proved that if the shear viscosity $${\mu}$$ is a positive constant and the bulk viscosity $${\lambda}$$ is the power function of the density, that is, $${\lambda=\rho^{\beta}}$$ with $${\beta \in [0,1],}$$ then the Cauchy problem of the two-dimensional compressible Navier–Stokes equations admits a unique global strong solution provided that the initial data are of small total energy. This result can be regarded as the extension of the well-posedness theory of classical compressible Navier–Stokes equations [such as Huang et al. (Commun Pure Appl Math 65:549–585, 2012) and Li and Xin ( http://arxiv.org/abs/1310.1673 ) respectively]. Furthermore, the large-time behavior of the strong solution to the Cauchy problem of the two-dimensional barotropic compressible Navier–Stokes equations had been also obtained.
Ending Page	27
Page Count	27
Starting Page	1
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	2
Volume Number	67
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-04-02
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics Vacuum Large-time behavior PDEs in connection with fluid mechanics Compressible Navier–Stokes equations Global existence Density-dependent viscosity Theoretical and Applied Mechanics Existence, uniqueness, and regularity theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

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