A note on stability shifting for the Muskat problem

Diego Córdoba; Javier Gómez-Serrano; Andrej Zlatoš

doi:10.1098/rsta.2014.0278

A note on stability shifting for the Muskat problem

Philos Trans A Math Phys Eng Sci. 2015 Sep 13;373(2050):20140278. doi: 10.1098/rsta.2014.0278.

Authors

Diego Córdoba¹, Javier Gómez-Serrano², Andrej Zlatoš³

Affiliations

¹ Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera, 13-15, 28049 Madrid, Spain Department of Mathematics, Princeton University, 804 Fine Hall, Washington Road, Princeton, NJ 08544, USA dcg@icmat.es.
² Department of Mathematics, Princeton University, 610 Fine Hall, Washington Rd, Princeton, NJ 08544, USA.
³ Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA.

Abstract

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L(∞) norm of the derivative of the initial condition that develop a turning singularity.

Keywords: Muskat problem; Rayleigh–Taylor; incompressible fluid; interface; porous media.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.