**Prof. Andrew Acker**

Wichita State University

**"On the Existence of Convex Classical Solutions for the Generalized Prandtl-Batchelor Free-boundary Problem"**

**Abstract:**

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 unknown boundary of the vortex core is a closed curve along which

,

where and denote, respectively, the exterior and interior flow-speeds along and is a given positive
constant. The existence results all apply to the natural multidimensional mathematical generalization of the above
problem.
#### Friday, November 17, 2000

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 2000]