CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

doi:10.1016/S0252-9602(12)60019-8

Abstract

Abstract:

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coe?cient. For regular initial data, we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically. When initial density is piecewise regular with jump discontinuity, we show that there exists a unique global piecewise regular solution. In
particular, the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t → +∞.

Key words: Navier-Stokes equations, discontinuous initial data

CLC Number:

35B40

LIAN Ru-Xu, LIU Jian, LI Hai-Liang, XIAO Ling. CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J].Acta mathematica scientia,Series B, 2012, 32(1): 315-324.

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