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Global entropy solution for the system of isothermal self-gravitating isentropic gases

Published online by Cambridge University Press:  14 July 2008

Dehua Wang  and
Zejun Wang
Dehua Wang
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA ([email protected])
Zejun Wang
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, People's Republic of China ([email protected])
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Abstract

The global entropy solution to the radial motion of isothermal self-gravitating gases is studied. A transformation of variables is applied. The global approximate solutions are constructed by a generalized shock-capturing scheme. The source terms include an integral which is non-local and is carefully estimated. The uniform estimate of the approximate solutions is obtained. The convergence of the approximate solutions is proved by the compensated compactness method. The global existence of weak entropy solution with large $L^{\infty}$ initial data is established. The solution allows a possible vacuum state.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 2 , April 2008 , pp. 407 - 426
Copyright
2008 Royal Society of Edinburgh

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