Non-isothermal lubrication problem with Tresca fluid–solid interface law. Part I

We consider the stationary equations for a non-isothermal Newtonian and incompressible fluids, in a three-dimensional bounded domain. The problem is governed by a coupled system involving a balance of linear momentum and the heat energy with Tresca free boundary friction conditions. Existence, uniqueness and regularity of the weak solution to this coupled problem are proved.