Wichita State University
On the existence of convex classical solutions for the generalized Prandtl-Batchelor free-boundary problem.
We discuss an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity is embedded in a closed irrotational flow inside a closed, convex vessel in the Euclidian plane. The unknown boundary of the vortex core is a closed curve along which the square of the outer tangential flow-speed minus the square of the inner tangential flow-speed is a positive constant. The existence results all apply to the natural multidimensional mathematical generalization of the above problem.