A Study of Weak Solutions and their Regularizations by Numerical Methods
Final rept. 1 Jul 1992-30 Jun 1993
OHIO STATE UNIV COLUMBUS DEPT OF MATHEMATICS
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Consider the incompressible Euler equations with vortex sheet initial data. For this initial value problem, there are a number of outstanding conjectures This initial value problem does not have a unique weak or measure- valued solution, a selection principle is required to pick out a unique solution. The limit of vanishing viscosity in the Navier Stokes equations provides the correct selection principle, and different regularizations, such as adding viscosity or smoothing the initial vortex sheet, may converge to different limits as the regularization tends to zero.
- Fluid Mechanics
- Plasma Physics and Magnetohydrodynamics