Analysis of a mixed boundary value problem for a stationary model of convection with variable viscosity and diffusion coefficients

A boundary value problem is considered for a nonlinear mass transfer model that generalizes the classical Boussinesq approximation under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions conditions for the concentration of the substance. 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 similar problems that ensure the local uniqueness of weak solutions are given.