Vanishing viscosity limit for incompressible Navier-Stokes equations with Navier boundary conditions for small slip length

In this paper, we will analyze the vanishing viscosity limit of the incompressible Navier-Stokes equations with the Navier slip boundary conditions in a bounded domain of R-2. When the slip length is smaller than or equal to the order of viscosity, by using an energy method and developing Kato's approach given in the work of Kato [Math. Sci. Res. Inst. Publ. 2, 85-98 (1984)], we obtain several conditions to guarantee that the solution of the Navier-Stokes equations with the Navier slip boundary conditions goes to the solution of the associated problem of the Euler equations in the energy space L-2 uniformly in time, as the viscosity goes to zero. Published by AIP Publishing.