Diego Cordoba (ICMAT, Madrid)

Finite time singularities in incompressible fluid interfaces

Abstract: We consider the evolution of an interface generated between two immiscible, incompressible fluids. Specifically we study the Surface Quasi-geostrophic equation (a sharp front of cold and hot air), the Muskat equation (the interface between oil and water in sand) and the water wave equation (interface between water and vacuum). For both Muskat and water wave equations we show the existence of smooth initial data for which the smoothness of the interface breaks down in finite time.