Weak shocks of a BGK kinetic model for isentropic gas dynamics

Carlota M. Cuesta; Sabine Hittmeir; Christian Schmeiser

doi:10.3934/krm.2010.3.255

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2010, Volume 3, Issue 2: 255-279. Doi: 10.3934/krm.2010.3.255

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Weak shocks of a BGK kinetic model for isentropic gas dynamics

1.
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Facultad de Ciencias, Universidad Autónoma de Madrid, Crta. Colmenar Viejo Km 15, 28049, Madrid
2.
Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstr. 8-10, 1040 Wien
3.
University of Vienna, Faculty for Mathematics, Nordbergstraße 15, 1090 Wien

Received: August 31, 2009

Revised: December 31, 2009

Published: May 2010

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Abstract

We consider a one-dimensional BGK model as a regularization for the isentropic system of gas dynamics. Existence and dynamic stability of small amplitude travelling waves of the kinetic transport equation are proven. Their macroscopic moments approximate viscous shock profiles for the isentropic system. These results are also extended to the isothermal case.

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Mathematics Subject Classification: Primary: 35Q72, 35L65; Secondary: 82C27, 35B40.

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