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Viscous limits to piecewise smooth solutions for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids. (English) Zbl 1188.35137

The present paper deals with a study of the asymptotic equivalence between the solutions of the compressible Navier-Stokes equations and the compressible Euler equations. The zero dissipation limit problem for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids is investigated. It is shown that the piece-wise smooth solutions of the inviscid Euler equations with finitely many non-interacting shocks satisfying the entropy condition are strong limits of solutions of the one-dimensional Navier-Stokes equations as the viscosity and heat-contactivity coefficients tend to zero.

MSC:

35Q30 Navier-Stokes equations
35Q31 Euler equations
76N15 Gas dynamics (general theory)
35B40 Asymptotic behavior of solutions to PDEs
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