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The inviscid limit to a contact discontinuity for the compressible Navier-Stokes-Fourier system using the relative entropy method. (English) Zbl 1333.35165

The authors study the monodimensional full compressible Navier-Stokes-Fourier system. They are especially interested in the zero heat conductivity limit to a contact discontinuity. The applied method represents an extension of the relative entropy method. No smallness assumptions on the discontinuity are provided. The bounded variation norm of the initial data must not be small. In the paper under review, it was shown that for arbitrary viscosity \(\nu \geq 0\) the solution of the compressible Navier-Stokes-Fourier system converges, if the heat conductivity \(\kappa\) tends to zero. The authors prove a decay rate of \({\kappa}^{1/2}\). As a consequence, they obtain that the heat conductivity dominates the dissipation in the regime of the limit to a contact discontinuity. Concerning a discontinuous solution for a system, it is a first result of an asymptotic limit which uses the relative entropy.
The paper is not large. The bibliography contains 42 items including 3 monographs.

MSC:

35Q30 Navier-Stokes equations
76N99 Compressible fluids and gas dynamics
35L65 Hyperbolic conservation laws
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References:

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