Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (4): 936-942.doi: 10.1016/S0252-9602(13)60052-1

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A NOTE ON THE EXISTENCE OF STATIONARY SOLUTIONS OF THE COMPRESSIBLE EULER-POISSON EQUATIONS WITH 6/5 < γ <|2

 XIANG Jian-Lin   

  1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China
  • Received:2012-07-20 Online:2013-07-20 Published:2013-07-20
  • Supported by:

    This work is supported by the Fundamental Research Funds for the Central Universities (2011-1a-021).

Abstract:

This paper is concerned with the system of Euler-Poisson equations as a model to describe the motion of the self-induced gravitational gaseous stars. When 6/5 < γ < 2, under the weak smoothness of entropy function, we find a sufficient condition to guarantee the existence of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy.

Key words: Euler-Poisson equations, stationary solutions, existence

CLC Number: 

  • 35Q35
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