The general problem of a perfect incompressible fluid motion with vortex areas and variant constant vorticities is formulated. The M.A. Goldshtiks variational approach is considered on research of dual problems for flows with vortex and potential are
as that describe detached flow and a motion model of a perfect incompressible fluid in field of Coriolis forces.
In this work there are considered model problems for two nonlinear equations, which type depends on the solution. One of the equations may be called a nonlinear analog of the Lavrentev-Bitsadze equation.
