Seminario EDPs y Mecánica de Fluidos

Gravity Unstable Muskat Bubbles

Ponente:  Neel Patel (ICMAT)
Fecha:  jueves 18 de noviembre de 2021 - 12:00
Lugar:  Aula Naranja (ICMAT)


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.