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arXiv · 2103.02474

Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem

Thomas Alazard·Quoc-Hung Nguyen
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Abstract

We exhibit a new decomposition of the nonlinearity for the Muskat equation and use it to commute Fourier multipliers with the equation. This allows to study solutions with critical regularity. As a corollary, we obtain the first well-posedness result for arbitrary large data in the critical space $\dot{H}^2(\mathbb{R}^2)\cap W^{1,\infty}(\mathbb{R}^2)$. Moreover, we prove the existence of solutions for initial data which are not Lipschitz.

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Thomas Alazard, Quoc-Hung Nguyen. 2021-03-03. Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem. https://arxiv.org/abs/2103.02474

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