The Cauchy problem for the compressible Navier-Stokes equations in the \(L_p\)-framework
type: Item
instance of: scholarly article
title: The Cauchy problem for the compressible Navier-Stokes equations in the \(L_p\)-framework
zbMATH Open document ID: 1048.35065
DOI: 10.1016/S0362-546X(02)00270-5
author: Piotr Bogusław Mucha
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The author considers compressible Navier-Stokes equations describing the motion of isentropic viscous fluid in the whole space. Using a priori time-independent energy estimates in anisotropic Sobolev spaces, the global in time existence of regular solutions is proved under some smallness assumptions. These solutions are close to nontrivial equilibrium solutions. The result is shown to be sharp in the \(L_p\)-framework.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 1880014
zbMATH Keywords: time-independent energy estimates
zbMATH Keywords: anisotropic Sobolev spaces
zbMATH Keywords: existence
zbMATH Keywords: equilibrium solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1880014