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

Abstract

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

14 pages

References in corpus (2)

• On the well-posedness of the incompressible density-dependent Euler equations in the $L^p$ framework
• On 3D Lagrangian Navier-Stokes $\alpha$ model with a Class of Vorticity-Slip Boundary conditions