## Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions.(English)Zbl 0992.35067

This paper deals with the study of the so-called incompressible limit for solutions of the compressible isentropic Navier-Stokes equations. The limit of global weak solutions in a bounded domain with homogeneous Dirichlet boundary conditions on the velocity, as the Mach number goes to zero, is studied. It is shown that the velocity converges weakly in $$L^2$$ to a global weak solution of the incompressible Navier-Stokes equations. The convergence in $$L^2$$ is strong under some geometric assumptions on the domain.

### MSC:

 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

### Keywords:

Navier-Stokes equations; Dirichlet boundary conditions
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