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

摘要

In this article, we study the solutions of the damped Navier-Stokes equation with the Navier slip boundary condition in a bounded domain Omega in R-3 with sufficiently smooth boundary. We employ theGalerkinmethod to approximate the solutions of the damped Navier-Stokes equations with the Navier-slip boundary conditions. The existence of the solutions is global for beta = 1. We also established the regularity of the solutions for beta >= 3, and the uniqueness of the solutions for beta >= 1.