# Accession Number:

## ADA158149

# Title:

## The Uniqueness of Hill's Spherical Vortex.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1985-05-01

# Pagination or Media Count:

## 50.0

# Abstract:

The only explicit exact solution of the problem of steady vortex rings is that found, for a particular case, by Hill in 1984 it solves a semilinear elliptic equation, of order two, involving a Stokes stream function psi r,z and a non-linearity sub H psi that has a simple discontinuity at psi 0. This paper proves that a any weak solution of the corresponding boundary-value problem is Hills solution, modulo translation along the axis of symmetry r 0, b any solution of the isoperimetric variational problem in another paper is a weak solution, indeed, any local maximizer is a weak solution. The result b is not immediate because f sub H is discontinuous consequently, the functional that is maximized is not Frechet differentiable on the whole Hilbert space in question. Additional keywords Fluid velocity TransformationsMathematics and Variational principles. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics