Steady-state solutions for the Muskat problem

Collect Math. 2023;74(2):313-321. doi: 10.1007/s13348-021-00348-z. Epub 2022 Mar 8.

Abstract

In this paper we study the existence of stationary solutions for the Muskat problem with a large surface tension coefficient. Ehrnstrom, Escher and Matioc studied in Mats Ehrnström (Methods Appl Anal 20:33-46, 2013) that there exists solutions to this problem for surface tensions below a finite value. In these notes we go beyond this value considering large surface tension. Also by numerical simulation we show some examples that explains the behavior of solutions.

Keywords: Fingering patterns; Muskat problem; Periodic solution; Steady state solutions.