The Viscosity Dependence On The Density Of The Local Strong Solution Of The Navier-stokes Equations, Existence And Uniqueness,

We study strong solutions of the isentropic compressible Navier-Stokes equations with a density-dependent viscosity in a bounded domainΩof R~3.We considerThe main contents of the paper include the following two parts:Frist,We linearize the above equations and use the semi-discreate Galerkin method to prove the existence and uniqueness of the linearized problem.Sencond, we construct the approximate solutionsby using iterative method and prove that the approximate solutions will converge to a strong solution of the original problem (*) and get the local existence and uniqueness of the strong solution of the original problem.