Noncoercive Stationary Navier–Stokes Equations of Heat-Conducting Fluids Modeled by Hemivariational Inequalities: An Equilibrium Problem Approach

Abstract

In this paper, we study the existence of solutions for noncoercive stationary Navier–Stokes equations of heat-conducting fluids with nonmonotone boundary conditions modeled by hemivariational inequalities. Our method is new and differs from most of the existing techniques developed in the literature. It is based on a recent approach developed on the existence of solutions for mixed equilibrium problems described by the sum of a maximal monotone bifunction and a pseudomonotone bifunction in the sense of Brezis. We introduce a Browder–Tikhonov regularization method for mixed equilibrium problems by means of the duality mapping with gauge function $$\mu (t)$$. By using this regularization procedure and techniques from the recession analysis, we study the existence of solutions for the problem considered in this paper.