ZERO DISSIPATION LIMIT TO A RIEMANN SOLUTION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS

doi:10.1016/S0252-9602(17)30067-X

Abstract

Abstract:

For the general gas including ideal polytropic gas, we study the zero dissipation limit problem of the full 1-D compressible Navier-Stokes equations toward the superposition of contact discontinuity and two rarefaction waves. In the case of both smooth and Riemann initial data, we show that if the solutions to the corresponding Euler system consist of the composite wave of two rarefaction wave and contact discontinuity, then there exist solutions to Navier-Stokes equations which converge to the Riemman solutions away from the initial layer with a decay rate in any fixed time interval as the viscosity and the heat-conductivity coefficients tend to zero. The proof is based on scaling arguments, the construction of the approximate profiles and delicate energy estimates. Notice that we have no need to restrict the strengths of the contact discontinuity and rarefaction waves to be small.

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

Hakho HONG, Teng WANG. ZERO DISSIPATION LIMIT TO A RIEMANN SOLUTION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS[J].Acta mathematica scientia,Series B, 2017, 37(5): 1177-1208.

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