Seminar on PDEs and Fluid Mechanics
Mixing solutions for unstable Muskat data with viscosity jump
Speaker: Paula Luna (Universidad de Sevilla)Date: Thursday, 12 November 2026 - 15:00Place: Aula Naranja, ICMAT
Abstract:
When two fluids of different densities and viscosities meet in a porous medium, their interface may become unstable and develop fingers, a phenomenon known as the Saffman–Taylor instability. In this regime, the classical Muskat problem is ill-posed. We construct mixing solutions to the incompressible porous media equation with density and viscosity jumps, starting from fully unstable Muskat data. The mixing zone grows linearly in time around an evolving central interface. A key ingredient is to invert the Birkhoff–Rott operator in terms of the Saffman–Taylor function rather than the vorticity, which considerably simplifies the analysis. This is a joint work with Francisco Mengual.
