The Stationary Navier–Stokes–Boussinesq System with a Regularized Dissipation Function

A boundary value problem is studied for a mathematical model describing the nonisothermal steady-state flow of a viscous fluid in a 3D (or 2D) bounded domain with locally Lipschitz boundary. A feature of the heat and mass transfer model considered is that a regularized Rayleigh dissipation function is used in the energy balance equation. This allows us to take into account the energy dissipation that occurs due to the viscous friction effect. A theorem on the existence of a weak solution is proved under natural assumptions on the model data. Moreover, we establish extra conditions guaranteeing that the weak solution is unique and/or strong.