Speaker: Xiaoming Wang.
Title: Singular Perturbation Problems in Fluid Dynamics.
Affiliation: Iowa State University.
Date: Friday, January 24, 2003.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.

Abstract. Real world fluid problems are usually very complex and often turbulent. They usually involve many scales both in time and in space. Thus various approximations are used to make progress on these highly nonlinear problems. These approximations are usually made in regimes where certain physical parameters are large or small which implies separation of scales. However, many of the approximations are singular in the sense that there are singular structures emerging in the limiting process. We illustrate these phenomena via two examples: the boundary layer phenomena associated with incompressible flows at small kinematic viscosity and the initial layer phenomena associated with convective flows at large Prandtl number. Simplified dynamics will be derived via formal asymptotic expansions together with compelling arguments on their validity. These formal results are backed by rigorous analysis.