Study On Vanishing Density Limit For The 3D Nonhomogeneous Incompressible Fluids With A Slip Boundary Condition

This paper investigate the 3D nonhomogeneous incompressible fluid in a flat domain with a slip boundary condition, hence, we add a compatible boundary condition of the density, and proof the existence of weak and strong solution and the uniqueness of the solution. In addition, we obtain the higher regularity. As the density limit tends to 1, the limit of the incompressible nonhomogeneous fluid with a slip boundary condition tends to the limit of the classical Navier-Stokes equations.