Rigidity of Acute Angled Corners for One Phase Muskat Interfaces

2021/11/17 by Siddhant Agrawal, Neel Patel, Agrawal, Siddhant +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Fluid Dynamics and Thin Films #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2111.09291

Abstract

We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. We prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle corners or cusps. Moreover, we show that isolated corners/cusps on the interface must be rigid, meaning the angle of the corner is preserved for a finite time, there is no rotation at the tip, the particle at the tip remains at the tip and the velocity of that particle at the tip points vertically downward.

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