On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
type: Item
instance of: scholarly article
title: On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
zbMATH Open document ID: 0860.35098
DOI: 10.1007/BF02106835
author: V. A. Vajgant
author: A. V. Kazhikhov
published in: Siberian Mathematical Journal
publication date: 1996-10-15T00:00:00Z
review text: The authors study the 2d Navier-Stokes system for a barotropic compressible fluid with constant dynamical viscosity and variable volume viscosity depending on the density of the fluid. For studying the ``time-global'' problem, the authors obtain a priori estimates with constants depending only on the data of the problem and the duration of the time interval and independent of the interval of existence of a local solution. Then, using already demonstrated theorems concerning existence and uniqueness for classical solutions on a sufficiently small time interval, the authors extend the local solution to the whole time interval. The existence of weak solutions is established by passage to the limit over a sequence of smooth solutions corresponding to the smoothed initial data.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 917153
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: global solutions
zbMATH Keywords: barotropic compressible fluid
zbMATH Keywords: variable volume viscosity
zbMATH Keywords: a priori estimates
zbMATH Keywords: local solution
reviewed by: Adrian Carabineanu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02106835
OpenAlex ID: W2019553990
description: scientific article; zbMATH DE number 917153