Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1298-1320.doi: 10.1016/S0252-9602(12)60100-3

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LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS

LIU Jian   

  1. Department of Mathematics, Capital Normal University, Beijing 100048, China
  • Received:2011-07-14 Revised:2011-10-26 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    This research is partially supported by the NSFC(10871134) and the AHRDIHL Project of Beijing Municipality (PHR201006107).

Abstract:

This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow den-sity vanishes continuously across the free boundary. Local (in time) existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.

Key words: Navier-Stokes equations, free boundary value problem, local existence

CLC Number: 

  • 35Q35
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