### 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 [24]. 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.

Original language | English (US) |
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Journal | Communications on Pure and Applied Mathematics |

DOIs | |

State | Accepted/In press - 2016 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*. https://doi.org/10.1002/cpa.21669

**On the Two-Dimensional Muskat Problem with Monotone Large Initial Data.** / Deng, Fan; Lei, Zhen; Lin, Fang-Hua.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the Two-Dimensional Muskat Problem with Monotone Large Initial Data

AU - Deng, Fan

AU - Lei, Zhen

AU - Lin, Fang-Hua

PY - 2016

Y1 - 2016

N2 - 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 [24]. 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.

AB - 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 [24]. 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.

UR - http://www.scopus.com/inward/record.url?scp=84992525074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992525074&partnerID=8YFLogxK

U2 - 10.1002/cpa.21669

DO - 10.1002/cpa.21669

M3 - Article

AN - SCOPUS:84992525074

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

ER -