Vanishing Viscosity Limit for Isentropic Navier-Stokes Equations with Density-dependent Viscosity

Details Vanishing Viscosity Limit for Isentropic Navier-Stokes Equations with Density-dependent Viscosity Vanishing Viscosity Limit for Isentropic Navier-Stokes Equations with Density-dependent Viscosity

2010-09-21

arxiv.org/abs/1009.3978v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isentropic compressible Euler equations. Based on several new uniform estimates to the viscous systems, in addition to the framework recently established by G. Chen and M. Perepelitsa, we justify that the finite energy solution of the isentropic compressible Euler equations for a large class of initial data can be obtained as the inviscid limit of the compressible Navier-Stokes equations even when the viscosity depends on the density.

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