Zero dissipation limit to rarefaction wave with vacuum for 1-D compressible Navier-Stokes equations


Li Mingjie, Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences, Beijing, China. 12 novembre 2010 14:00 edp 2:00:00
Abstract:

It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected with vacuum. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate is obtained. The proof consists of a scaling argument and elementary energy analysis, based on the underlying rarefaction wave structures.