On twodimensional and three dimensional axiallysymmetric rotational flows of an ideal incompressible fluid
Abstract
The solvability of equations describing stationary twodimensional and threedimensional axiallysymmetric 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 secondorder PDE with mixed boundary conditions solvable with the aid of monotonic and pseudomonotonic operators. Uniqueness and applicability of a weak solution are discussed.
 Publication:

Aplikace Matematiky, Applied Mathematics
 Pub Date:
 1977
 Bibcode:
 1977ApMat..22..199F
 Keywords:

 Axisymmetric Flow;
 Ideal Fluids;
 Incompressible Fluids;
 Three Dimensional Flow;
 Two Dimensional Flow;
 Vortices;
 Boundary Conditions;
 Boundary Value Problems;
 Continuity Equation;
 Equations Of Motion;
 Operators (Mathematics);
 Partial Differential Equations;
 Uniqueness Theorem;
 Fluid Mechanics and Heat Transfer