Nonlinear degenerate parabolic equations for a thermohydraulic model

Abstract

In this paper, we consider an initial boundary value problem for a system of second order partial differential equations. This system consists of the Navier-Stokes equations and a nonlinear heat equation. More precisely, we impose a nonlinear heat flux associated with a class of maximal monotone graphs with a Neumann boundary condition. We establish the conditions required to prove the existence of a solution for the given data.