Nonlinear Partial Differential Equations

Date: September 25, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Anna Mazzucato, Penn State University

Title: Nonlinear PDE's Seminar

Abstract:

Title: On the vanishing viscosity limit in incompressible flows

Abstract:
I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions. I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.