Solvability of inhomogeneous boundary problems for the stationary mass-transfer equations

Boundary value problems for stationary mass-transfer for viscous equations are considered under nhomogeneous boundary conditions for the velocity and the concentration of the substance. The existence and uniqueness of a weak solution of the initial boundary value problem in a domain with a Lipshitz boundary is proved, exact apriori estimates of the solution are deduced and the regularity of the solution in the case of two dimensions is studied.