On the Two-Dimensional Muskat Problem with Monotone Large Initial Data
Analysis of PDEs
2016-09-27 v2
Abstract
We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [26]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function.
Keywords
Cite
@article{arxiv.1603.03949,
title = {On the Two-Dimensional Muskat Problem with Monotone Large Initial Data},
author = {Fan Deng and Zhen Lei and Fanghua Lin},
journal= {arXiv preprint arXiv:1603.03949},
year = {2016}
}
Comments
To appear in Comm. Pure and Appl. Math