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 result on concentration of vorticity at the boundary for symmetric flows and the justification of Prandtl approximation for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains, quantifying the effect of curvature on the pressure correction.
This talk will be given in a joint Analysis/Applied Math and Computation seminar.