Steady-state fingering patterns for a periodic Muskat problem

2013/03/27 by Ehrnstrom, Mats, Escher, Joachim, Matioc, Bogdan-Vasile · 1 citation
#34A12 #34C23 #34C25 #70K42 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1303.6724

Abstract

We study global bifurcation branches consisting of stationary solutions of the Muskat problem. It is proved that the steady-state fingering patterns blow up as the surface tension increases: we find a threshold value for the cell height with the property that below this value the fingers will touch the boundaries of the cell when the surface tension approaches a finite value from below; otherwise, the maximal slope of the fingers tends to infinity.

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• Well-posedness and Rayleigh-Taylor instability of the two-phase periodic quasistationary Stokes flow

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