Drop"s movement in an inconspicuous fluid

The task of the evolution of two viscous non -laughing liquids with an unknown surface of the section belongs to the currently studied class of tasks with free boundaries, since in it, along with the vector field of speeds and the pressure function of both liquids, the surface of their section is subject to determination. The theory of these tasks for the Vesse - Stox equations has only a little more than four decades in its development, although their production dates back to the classic works of the XIX. In the monograph, a general picture of the smoothness of problems that describe the simultaneous movement of two incompatible liquids is presented. In particular, a study of resolution in the spaces of Sobolev-Slobodetsky and Gölder of the initial-in-law tasks for the equations of Stox and Navier-Stakes in the limited areas with a closed boundary of the two medium audience of senior students, graduate students of the physicist faculties of universities, scientific and scientific employees