Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

The Muskat problem describes the evolution of the interface between two immiscible fluids in porous media, e.g. oil and water in soil. Neglecting surface tension, the well-posedness of this free boundary problem depends on the Rayleigh-Taylor condition. For fluids of differing densities, it is required that the denser fluid is below. Otherwise, the system is gravity unstable. We will consider the stability of a closed curve interface, or a bubble, in which the Rayleigh-Taylor condition cannot hold. Medium sized perturbations of circular bubbles are shown to be globally well-posed, instantly analytic and decay exponentially quickly to the circle shape.