On Generalized Energy Inequality of the Damped Navier–Stokes Equations with Navier Slip Boundary Conditions

Abstract

In this article, we deal with a damped Navier–Stokes equations in IR3 with slip boundary conditions. Sufficient conditions for the existence of the solutions to the Navier–Stokes system are established in a bounded domain Ω⊂IR3. Further, we show that the solutions derived by Rothe’s method are satisfying the local energy inequality.