Methods and Applications of Analysis

Viscous Limits to Piecewise Smooth Solutions for the Navier-Stokes Equations of One-dimensional Compressible Viscous Heat-conducting Fluids

Shixiang Ma

Full-text: Open access

Abstract

In this paper, we study the zero dissipation limit problem for the Navier-Stokes equations of one-dimensional compressible viscous heat-conducting fluids. We prove that if the solution of the inviscid Euler equations is piecewise smooth with finitely many noninteracting shocks satisfying the entropy condition, then there exist solutions to Navier-Stokes equations which converge to the inviscid solution away from shock discontinuities at a rate of $\epsilon^1$ as the viscosity $\epsilon$ tend to zero, provided that the heat-conducting coefficient $k = 0($\epsilon$).

Article information

Source
Methods Appl. Anal., Volume 16, Number 1 (2009), 1-32.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.maa/1255958148

Mathematical Reviews number (MathSciNet)
MR2556826

Zentralblatt MATH identifier
1188.35137

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76N15: Gas dynamics, general

Keywords
Compressible Navier-Stokes equations compressible Euler equations viscous limit noninteracting shocks

Citation

Ma, Shixiang. Viscous Limits to Piecewise Smooth Solutions for the Navier-Stokes Equations of One-dimensional Compressible Viscous Heat-conducting Fluids. Methods Appl. Anal. 16 (2009), no. 1, 1--32. https://projecteuclid.org/euclid.maa/1255958148


Export citation