Navier–Stokes equations with nonhomogeneous boundary conditions in a convex bi-dimensional domain

Abstract

We prove the existence of a weak solution to Navier–Stokes equations describing the isentropic flow of a gas in a convex and bounded region, $\Omega \subset {\mathbf{R}}^2$, with nonhomogeneous Dirichlet boundary conditions on $\partial \Omega$. These results are also extended to flow domain surrounding an obstacle.