Plenary Talk 2: October 1, Saturday 2:00pm-3:00pm, Click Hall, Alumni Center.
Title: Boundary layers and the vanishing viscosity limit for 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). I will present cases of flows where Prandtl approximation and the vanishing viscosity limit can be rigorous justified, in particular a result on concentration of vorticity at the boundary for symmetric flows and convergence for an Oseen-type equation in smooth domain, showing the effect of curvature on the pressure corrector.
Biography: Anna Mazzucato is Professor of Mathematics at Penn State University. She is an applied analyst working on PDE problems in continuum mechanics. Prior to joining Penn State in 2003, she was a Gibbs Instructor at Yale University and a Postdoctoral Fellow at the IMA and MSRI. She obtained her PhD from the University of North Carolina-Chapel Hill in 2000 under the direction of Michael Taylor. In 2011 she received the Ruth I. Michel Memorial Prize from the AWM and Cornell University and was elected SIAM Fellow in 2021. She is on the editorial boards of several journals, including the SIAM Journal on Mathematical Analysis.
For more detail, please visit Professor Mazzucato's Website: http://www.personal.psu.edu/alm24/