Vacuum states for compressible flow

Tai-Ping Liu; Zhouping Xin; Tong Yang

doi:10.3934/dcds.1998.4.1

Article Contents

1998, Volume 4, Issue 1: 1-32. Doi: 10.3934/dcds.1998.4.1

This issue Previous Article Next Article Singular continuous spectrum and quantitative rates of weak mixing

Vacuum states for compressible flow

1.
Department of Mathematics, Stanford University
2.
Department of Mathematics, Courant Institute, New York University
3.
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

Received: May 31, 1997

Published: December 1997

Abstract Related Papers Cited by

Abstract

In this paper we study the evolutions of the interfaces between gases and the vacuum for both inviscid and viscous one dimensional isentropic gas motions. The local (in time) existence of solutions for both inviscid and viscous models with initial data containing vacuum states is proved and some singular properties on the free surfaces separating the gas and the vacuum are obtained. It is found that the Euler equations are better behaved near the vacuum than the compressible Navier-Stokes equations. The Navier-Stokes equations with viscosity depending on density are introduced, which is shown to be well-posed (at least locally) and yield the desired solutions near vacuum.

Keywords:

Mathematics Subject Classification: 35Qxx.

Citation:

Article Metrics

HTML views() PDF downloads(420) Cited by(0)

Vacuum states for compressible flow

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Vacuum states for compressible flow

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content