ANALYSIS OF A MIXED BOUNDARY VALUE PROBLEM FOR A STATIONARY MODEL OF SUBSTANCE CONVECTION WITH VARIABLE VISCOSITY AND DIFFUSION COEFFICIENTS

In this paper, we consider a boundary value problem for a nonlinear mass transfer model that generalizes the classical Boussinesq approximation under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for the substance concentration. It is assumed that the viscosity and diffusion coefficients and the buoyancy force in the model equations depend on the concentration. A mathematical apparatus for studying the problem is developed and used to prove the theorem on the global existence of a weak solution. Sufficient conditions for the problem under study that ensure the local uniqueness of weak solutions are given.