Global well-posedness for the one-phase Muskat problem

PDE Seminar
Tuesday, April 18, 2023 - 3:00pm for
Skiles 006
Huy Nguyen – University of Maryland, College Park – hnguye90@umd.edu
Gong Chen


We will discuss the one-phase Muskat problem concerning the free boundary of Darcy fluids in porous media. It is known that there exists a class of non-graph initial boundary leading to self-intersection at a single point in finite time (splash singularity). On the other hand, we prove that the problem has a unique global-in-time solution if the initial boundary is a periodic Lipschitz graph of arbitrary size. This is based on joint work with H. Dong and F. Gancedo.