Hyunwoo Kwon
Brown University
Title
Global well-posedness of the one-phase Muskat problem with surface tension
Abstract
The one-phase Muskat problem describes the motion of the interface separating a wet region from a dry region within a porous medium, a process governed by Darcy’s law. Although physically essential, the inclusion of surface tension introduces an additional challenge. We prove small-data global well-posedness of the problem in the subcritical regime. Moreover, the solution converges to zero in Lipschitz norm as $t\rightarrow\infty$. To the best of our knowledge, this work constitutes the first global well-posedness result for the one-phase Muskat problem with surface tension. If we have enough time, I will present another interesting numerical experiment regarding this problem. This talk is based on the joint work with Hongjie Dong (Brown).
Zoom Link: https://osu.zoom.us/j/91783892334?pwd=bXp0v6WgiS9AObyBQy6wkpZVaw5BI0.1
