Two global-in-time results for Muskat

Abstract: In this talk we consider the Muskat problem, modeling the dynamics of two incompressible immiscible fluids in porous media. First, we consider fluids of different densities. This case has been extensively studied recently, in particular because its very interesting features. The fluids can be stable, enter into unstable regime and next to develop finite time singularities. We show that this scenario is not possible in 3D for arbitrary slope and small data, providing global-in-time critical solutions. Second, we deal with capillarity forces with viscosity-density fluids. This case is fundamental in order to understand fingering phenomena. For gravity unstable situations, we show that 2D bubbles exist for all time for initial data given by a wide balance between small norm, density, viscosity and surface tension.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom