Affiliation - University of Pennsylvania
Title of Talk - Analysis of Moving Interfaces in Incompressible Flows
Interfaces that evolve with a fluid flow abound in nature and engineering. They are subject to intense research in many different fields, from meteorology to medical sciences or the petroleum industry. However, the mathematical analysis of these free boundary problems is still emerging, which impedes a deeper understanding necessary for accurate numerical methods. In this talk, we will give an overview of certain fluid-fluid and fluid-structure interfaces problem (inhomogeneous Navier-Stokes, Boussinesq, Muskat and Peskin models). The focus is placed on global-in-time results (versus finite-time singularities), with initial interfaces that are not just small perturbations. The analysis is thus purely nonlinear. Particular attention is given to initial data in critical spaces and the challenging non-local effects of viscosity contrasts.