Existence and uniqueness results for a coupled problem related to the stationary Navier-Stokes System

Abstract

In this paper, we consider some systems which are close to the stationary Navier-Stokes equations. The structure of these systems is the following: An N-dimensional equation for motion, the incompressibility condition and a scalar equation involving an additional unknown, k = k(x). Among other things, they serve to model the behavior of certain turbulent flows. Our main interest concerns existence and uniqueness. The main difficulties are due to the structure of the scalar equation; in partic- ular, the right side is typically in L1 and, furthermore, there are nonlinear terms of the kind ∇ · (μ(k)∇k) and ∇ · (B(k)), where μ and B are general continuous functions.