On one two-dimensional binary mixture’s motion in a flat layer

In this paper is estimated a special solution for solving thermal diffusion equations, that describe motion of binary mixture in a flat layer. When Reynolds number ($Re\to0$) is small, it is possible to simplify these equations to some easier problems. In solving process to find pressure it is necessary to solve an inverse problem. Answers for non-stationary regime are presented in trigonometric Fourier series.