The Non-Incompressibility on Heat-Conducting Fluids. The Stationary Case

This work deals with generalized viscous flows that can only undergo isochoric motions in isothermal processes, but can sustain motions that are not necessarily isochoric in processes that are not isothermal. The heat-conducting Stokes and Bingham fluids appear as a direct application. The method used here is a combination of a fixed point argument, the Uzawa-type algorithm and the optimization theory. The pressure is found as a limit of a sequence such that satisfies a constraint condition.