The Viscid Wave Equations Convergence To The Incompressible Navier-Stokes Problem

In this paper, we introduce damped wave equations defined on R2, we get the global existence for this damped wave equations under suitable assumptions on the initial data. The main conclusion of this paper as follows, the solutions for the damped wave equations convergence to the solution for the Navier-Stokes equations in some sense if their initial data satisfy some suitable relations and assumptions.The purpose of this paper is to give us two main point respectively in dimension2. First, we prove the global existence for the damped wave equations under suitable smallness assumptions on the initial data. Then, we get the convergence from this solu-tions towards the solution for the Navier-Stokes equations. Since the initial data is less regularity, we improve the energy estimate according to a called modulated energy.