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

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 Brézis. We introduce a Browder–Tikhonov regularization method for mixed equilibrium problems by means of the duality mapping with gauge function μ(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.