Mixing solutions for the Muskat problem with variable speed-Reference-Cited by-同舟云学术

Mixing solutions for the Muskat problem with variable speed

Published:2020-12-12 Issue:3 Volume:21 Page:3289-3312
ISSN:1424-3199
Container-title:Journal of Evolution Equations
language:en
Short-container-title:J. Evol. Equ.

Author:

Noisette Florent,Székelyhidi László^ORCID

Abstract

AbstractWe provide a quick proof of the existence of mixing weak solutions for the Muskat problem with variable mixing speed. Our proof is considerably shorter and extends previous results in Castro et al. (Mixing solutions for the Muskat problem, 2016, arXiv:1605.04822) and Förster and Székelyhidi (Comm Math Phys 363(3):1051–1080, 2018).

Funder

H2020 European Research Council

Publisher

Springer Science and Business Media LLC

Subject

Mathematics (miscellaneous)

Link

https://link.springer.com/content/pdf/10.1007/s00028-020-00655-1.pdf

Reference30 articles.

1. Alazard, T. and Lazar, O. Paralinearization of the Muskat equation and application to the Cauchy problem. Arch. Ration. Mech. Anal. (2020), 237 (2), 545–583.

2. Alazard, T. and Nguyen, Q.-H. On the Cauchy problem for the Muskat equation. II: Critical initial data. arXiv:2009.08442 (2020)

3. Arnaiz, V., Castro, Á., and Faraco, D. Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime. arXiv:2001.06361 (2020)