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Title: Global well‐posedness for the one‐phase Muskat problem
Abstract The free boundary problem for a two‐dimensional fluid permeating a porous medium is studied. This is known as the one‐phase Muskat problem and is mathematically equivalent to the vertical Hele‐Shaw problem driven by gravity force. We prove that if the initial free boundary is the graph of a periodic Lipschitz function, then there exists a global‐in‐time Lipschitz solution in the strong sense and it is the unique viscosity solution. The proof requires quantitative estimates for layer potentials and pointwise elliptic regularity in Lipschitz domains. This is the first construction of unique global strong solutions for the Muskat problem with initial data of arbitrary size.  more » « less
Award ID(s):
2205734 2055244
PAR ID:
10491949
Author(s) / Creator(s):
; ;
Publisher / Repository:
Wiley
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
76
Issue:
12
ISSN:
0010-3640
Page Range / eLocation ID:
3912 to 3967
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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