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Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data

Published online by Cambridge University Press:  12 July 2007

Song Jiang  and
Alexander Zlotnik
Song Jiang
Affiliation:
Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, People's Republic of China (jiang@iapcm.ac.cn)
Alexander Zlotnik
Affiliation:
Department of Mathematical Modelling, Moscow Power Engineering Institute, Krasnokazarmennaya 14, 111250 Moscow, Russia (zlotnik@apmsun.mpei.ac.ru)
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Abstract

We study the Cauchy problem for the one-dimensional equations of a viscous heat-conducting gas in the Lagrangian mass coordinates with the initial data in the Lebesgue spaces. We prove the existence, the uniqueness and the Lipschitz continuous dependence on the initial data of global weak solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 5 , October 2004 , pp. 939 - 960
Copyright
Copyright © Royal Society of Edinburgh 2004

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