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

Ma, Shixiang

Methods Appl. Anal. 16, No. 1, 1-32 (2009).

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.

Reviewer: Georg V. Jaiani (Tbilisi)

MSC:

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

Keywords:

compressible Navier-Stokes equations; compressible Euler equation; viscous limit; noninteracting shocks