On two-dimensional and three dimensional axially-symmetric rotational flows of an ideal incompressible fluid

The solvability of equations describing stationary two-dimensional and three-dimensional axially-symmetric rotational flows of an ideal incompressible fluid is investigated. Attention is focused on inner hydrodynamics problems. The system of PDE (continuity equations plus equations of motion) in energy form is supplemented with three types of boundary conditions complete in the sense that irrotational flow guarantees uniqueness. After the stream function is introduced, the problem is transformed to a boundary problem for quasilinear second-order PDE with mixed boundary conditions solvable with the aid of monotonic and pseudomonotonic operators. Uniqueness and applicability of a weak solution are discussed.