On the isentropic compressible Navier-Stokes equation
نویسندگان
چکیده
In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove the stability of weak solutions of the Saint-Venant model for shallow water.
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