A note on stability shifting for the Muskat problem.
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.
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.
Diego
D
Córdoba
Department of Mathematics, Princeton University, 610 Fine Hall, Washington Rd, Princeton, NJ 08544, USA.
Javier
J
Gómez-Serrano
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA.
Andrej
A
Zlatoš
Muskat problem; Rayleigh–Taylor; incompressible fluid; interface; porous media