Initial boundary value problems for vortex motion of an ideal fluid in bounded domains

The paper deals with the problem of vortex motion of an incompressible perfect fluid in bounded domains. The research is confined to chosen cases of steady velocity fields within rectangular, circular and elliptic regions with rigid boundaries. The solution to the initial-value problem of the fluid flow for the assumed velocity fields is the primary object of this paper. It is demonstrated that individual particles of the fluid have their own periods of motion and thus, one should be careful in describing such problems by means of discrete methods, especially in the Lagrangian variables. The problem discussed has its origin in numerical analysis of water waves by means of the finite difference or the finite element method.