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Abstract

The solvability of inhomogeneous liquid diffusion model based on the magnetic field is studied in this paper. Well-known results on the problem, describing the flow of a viscous incompressible fluid in an inhomogeneous magnetic field are presented. The solvability is studied by O.A. Ladyzhenskaya and V.A. Solonnikov, then these results were summarized in the works of S.S.
Sahaevwith the persistence of smoothness of the solution up to the boundary. In contrast to the above-mentioned problems in the case of an inhomogeneous liquid another equation is added related to the density of liquids. This problem is approximated by the method presented by S.S. Smagulov.Estimates of the rate of convergence of solutions of the problem to the solution of the original problem are given when splitting parameter tends to zero.