TY - JOUR
T1 - Vanishing Viscosity Limit of the Compressible Navier-Stokes Equations for Solutions to a Riemann Problem
AU - Huang, Feimin
AU - Wang, Yi
AU - Yang, Tong
PY - 2012/2
Y1 - 2012/2
N2 - We study the vanishing viscosity limit of the compressible Navier-Stokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible Navier-Stokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the Navier-Stokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves. © 2011 Springer-Verlag.
AB - We study the vanishing viscosity limit of the compressible Navier-Stokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible Navier-Stokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the Navier-Stokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves. © 2011 Springer-Verlag.
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U2 - 10.1007/s00205-011-0450-y
DO - 10.1007/s00205-011-0450-y
M3 - RGC 21 - Publication in refereed journal
VL - 203
SP - 379
EP - 413
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -