Free Boundary Problems Arising in Fluid Mechanics

Abstract

Fluid mechanics is one of the classical areas in the study of partial differential equations and has been a vast subject of research in the last centuries. A relevant class of problems are those in which the evolution of fluids of different nature and their interaction is described through the dynamics of their common boundary. Such problems are called free-boundary problems. The key topic of this workshop deals with recent advances on the analysis of free-boundary problems which open up a whole new area of research activity. More precisely, we will address problems as the vortex-patch, the study of water waves, interface flows in porous media and Hele-Shaw cells as well as atmospheric front dynamics where the formation of finite time singularities is a fundamental open question.