Analytic treatment of some mathematical models of planar problems of the movement of liquid

In introduction the principles of creation of mathematical models of the movement of liquids and possible simplifications are briefly stated. Difficulties of research of process in a three-dimensional case are noted. Therefore in the main body of the article two planar problems of the movement of nonviscous incompressible liquid are considered. Mathematical models are Riemann-Hilbert problems for Cauchy-Riemann equation and adjoint Cauchy-Riemann equation. Theorems of existence and uniqueness of solutions of these problems are proved.