C O L L O Q U I U M
On 2-D Incompressible Singular Flows
Professor Zhouping Xin
The Chinese University
of Hong Kong, Hong
Kong
and
Courant Institute, NYU, USA
Abstract
Studies on the 2-dimensional incompressible fluid flows in which the vorticity fields change dramatically are of considerable
interests in the mathematical theory and applications. Well-known examples of
such flows include evolutions of vortex patches, vorrtex
sheets, and boundary layers, which provide good approximations for significant
parts of the flow fields in the mixing layers, trailing wakes, and near
physical boundaries, etc., at high Reynolds numbers. The main questions are the
existence of classical weak solutions and the structure of various approximate
solutions generated by either considerations or numerical methods. One of the
key issues is whether concentration phenomena can occur either for energy or vorticity. In this talk, I will survey the field and
present some recent results which include: hydrodynamical
limit of a Hamiltonian systems of interacting particles to classical weak
solutions for the 2-D incompressible Euler equations with a class of
"rough" initial data including vortex sheet data; the existence of
vortex sheets with reflection symmetry (This is the first existence result
involving two-sign vorticity); convergence of a class
of finite element methods for the evolution of vortex patches; and some new
global existence of weak solutions to the Prandtl's
boundary layer equations.
|
Date:
|
November 3, 2000 (Friday)
|
|
Time:
|
4:00 - 5:00pm
|
|
Place:
|
Room 517, Meng Wah
Complex
|
All are welcome