On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data

By Fan Deng, Zhen Lei, F. Lin. 2016

47 citations recorded by the source corpus.

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.© 2016 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/87e1807469f30c0c631e956aad1a1a74bc6b37dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Quoc-Hung Nguyen
2. Thomas Alazard
3. Omar Lazar
4. Stephen Cameron

In Computational Theory and Mathematics

1. Omar Lazar
2. Stephen Cameron
3. Quoc-Hung Nguyen
4. Thomas Alazard

Citations in the corpus

• A Paradifferential Approach for Well-Posedness of the Muskat Problem (2019, unknown): “Global weak solutions were obtained in [20, 29].”
• Endpoint Sobolev Theory for the Muskat Equation (2020, background): “[36], Cameron [15], Córdoba and Lazar [35], Gancedo and Lazar [38] which allowed arbitrary large slopes.”
• Global well-posedness for the two-dimensional Muskat problem with slope less than 1 (2017, background): “2 STEPHEN CAMERON Recently, [8] was also able to prove the existence of global weak solutions for arbitrarily large monotonic initial data.”
• Paralinearization of the Muskat Equation and Application to the Cauchy Problem (2019, background): “doba, Gancedo, Rodr´ıguez-Piazza and Strain for global well-posedness results assuming that the Lipschitz semi-norm is smaller than 1 (see also [15] where time decay of those solutions is proved). In [26], Deng, Lei and Lin proved the existence of global in time solutions with large slopes, assuming”