ZERO DISSIPATION LIMIT TO CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS

doi:10.1016/S0252-9602(15)30085-0

Abstract

Abstract:

The zero dissipation limit to the contact discontinuities for one-dimensional com-pressible Navier-Stokes equations was recently proved for ideal polytropic gas(see Huang et al. [15, 22] and Ma [31]), but there is few result for general gases including ideal polytropic gas. We prove that if the solution to the corresponding Euler system of general gas satisfying(1.4) is piecewise constant with a contact discontinuity, then there exist smooth solutions to Navier-Stokes equations which converge to the inviscid solutions at a rate of κ^1/4 as the heat-conductivity coefficient κ tends to zero. The key is to construct a viscous contact wave of general gas suitable to our proof(see Section 2). Notice that we have no need to restrict the strength of the contact discontinuity to be small.

Key words: zero dissipation limit, Navier-Stokes equations, contact discontinuity, general gas

CLC Number:

76N99

Hakho HONG. ZERO DISSIPATION LIMIT TO CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS[J].Acta mathematica scientia,Series B, 2016, 36(1): 157-172.

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