Abstract
We prove that as the viscosity and heat-conductivity coefficients tend to zero, respectively, the global solution of the Navier-Stokes equations for one-dimensional compressible heat-conducting fluids with centered rarefaction data of small strength converges to the centered rarefaction wave solution of the corresponding Euler equations uniformly away from the initial discontinuity.
Highlights
Compressible Navier-Stokes Equations, Vanishing Viscosity Limit, Scientific Research Publishing Inc
We study the asymptotic behavior, as the viscosity and heat-conductivity go to zero, respectively, of solutions to the Cauchy problem for the Navier-Stokes equations for a one-dimensional compressible heat-conducting fluid:
It is expected that a general weak entropy solution to the Euler equations should be limit of solutions to the corresponding Navier-Stokes equations with same initial data as the viscosity and heat conductivity tend to zero, respectively
Summary
College of Science, University of Shanghai for Science and Technology, Shanghai, China. How to cite this paper: Cui, S.F. (2018) Dissipation Limit for the Compressible Navier-Stokes to Euler Equations in OneDimensional Domains. Journal of Applied Mathematics and Physics, 6, 2142-2158. Received: October 2, 2018 Accepted: October 26, 2018 Published: October 29, 2018
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