Tuesday, November 22, 2011 - 3:05pm
1 hour (actually 50 minutes)
In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.