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arXiv · 2310.14531

The regularity of the solutions to the Muskat equation: the degenerate regularity near the turnover points

Jia Shi
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Abstract

In this paper, we prove that if a solution to the Muskat problem with different densities and the same viscosity is sufficiently smooth, the solution is analytic in a region that degenerates at the turnover points, provided some additional conditions are satisfied. This paper studies the analyticity of the solution near turnover points, complementing the result in $[$Jia Shi. Regularity of solutions to the Muskat equation, Arch Rational Mech Anal 247, 36 (2023)$]$.

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Jia Shi. 2023-10-23. The regularity of the solutions to the Muskat equation: the degenerate regularity near the turnover points. https://arxiv.org/abs/2310.14531

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