INTERFACE BEHAVIOR OF COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS AND VACUM

doi:10.1016/S0252-9602(11)60287-7

Abstract

Abstract:

In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang [12] to the jump boundary conditions case.

Key words: interface, Navier-Stokes equations, vacuum

CLC Number:

35Q10

GUO Zhen-Hua, HE Wen. INTERFACE BEHAVIOR OF COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS AND VACUM[J].Acta mathematica scientia,Series B, 2011, 31(3): 934-952.

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