| Abstract: |
| We study the free boundary problem for 2D and 3D incompressible flow in porous media, known as the one-phase Muskat problem.
In the absence of surface tension, we prove that when the initial interface is given by a Lipschitz graph, there exists a unique global Lipschitz strong solution. When surface tension is included, we establish small-data global well-posedness and time-decay results in both the whole-space and periodic settings.
This talk is based on joint work with Francisco Gancedo (Universidad de Sevilla), Huy Q. Nguyen (University of Maryland), and Hyunwoo (Will) Kwon (Brown University). |
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