Vanishing Viscosity Limit For the 3D Nonhomogeneous Incompressible Navier-Stokes Equations With a Slip Boundary Condition

摘要

In this paper, we investigate the vanishing viscosity limit for the 3Dnonhomogeneous incompressible Navier-Stokes equations with a slip boundarycondition. We establish the local well-posedness of the strong solutions forinitial boundary value problems for such systems. Furthermore, the vanishingviscosity limit process is established and a strong rate of convergence isobtained as the boundary of the domain is flat. In addition, it is needed toadd some additional condition for density to match well the boundary condition.