Existence and uniqueness of solutions to the damped Navier-Stokes equations with Navier boundary conditions for three dimensional incompressible fluid

Abstract

In this article, we study the solutions of the damped Navier-Stokes equation with Navier boundary condition in a bounded domain Ω in R 3 with smooth boundary. The existence of the solutions is global with the damped term ϑ|u| β−1 u, ϑ > 0. The regularity and uniqueness of solutions with Navier boundary condition is also studied. This extends the existing results in literature.