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On the 2D Muskat Problem with Monotone Large Initial Data

Authors
  • Deng, Fan
  • Lei, Zhen
  • Lin, Fanghua
Type
Preprint
Publication Date
Mar 12, 2016
Submission Date
Mar 12, 2016
Identifiers
arXiv ID: 1603.03949
Source
arXiv
License
Yellow
External links

Abstract

We consider the evolution of two incompressible, immiscible fluids with different densities in porus media, known as the Muskat problem [21] which in 2D is analogous to the Hele-Shaw cell [26]. We first establish a local well-posedness result for initial data with asymptotics at spacial infinity and infinite energy. Then for large and monotone initial data, we establish the global existence of weak solutions by exploring a new maximum principle for the first derivative of the graph function. Our work is inspired by the recent interesting results in [13, 14, 15]. As far as we know, this is the first global large solution for a class of relatively general class of large data.

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