Local Existence and Uniqueness of Prandtl Equations
Speaker: Tak Kwong Wong
Location: Warren Weaver Hall 1302
Date: Tuesday, March 5, 2013, 11 a.m.
The Prandtl equations, which describe the boundary layer behavior of a viscous incompressible fluid near the physical wall, play an important role in the zero-viscosity limit of Navier-Stokes equations. In this talk we will discuss the local-in-time existence and uniqueness for the Prandtl equations in weighted Sobolev spaces under the Oleinik's monotonicity assumption. The proof is based on weighted energy estimates, which come from a new type of nonlinear cancellations between velocity and vorticity.