On Existence and Regularity of Solutions for a Stationary Navier-Stokes System Coupled to an Equation for the Turbulent Kinetic Energy

Abstract

We investigate a stationary model for turbulent flows, in which the Navier-Stokes system is coupled to an equation for the density of turbulent kinetic energy through a bounded coefficient of eddy viscosity. We prove the existence of weak solutions for which the gradients are higher integrable. The latter property allows us to prove that the model is well posed in the two dimensional case, provided that the external forcing remains sufficiently small.