Topics in an ideal fluid dynamics (Q814400)

The paper deals with the uniqueness problem for the Euler equations of an ideal incompressible fluid motion. The problem of reduction of the fluid equations of motion with respect to the vorticity integrals is considered as well. The two problems are discussed and only partial results are obtained. Namely, a counter-example is constructed which shows that the conditions of the uniqueness theorem is unimprovable within the framework of the energy method. In the two-dimensional case the Lagrangian equations of fluid dynamics are reduced to a single scalar equation for the generating function of the area preserving mapping corresponding to the fluid flow.