The Muskat problem with 𝐶¹ data

Chen, Ke; Nguyen, Quoc-Hung; Xu, Yiran

doi:10.1090/tran/8559

The Muskat problem with $C^1$ data
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by Ke Chen, Quoc-Hung Nguyen and Yiran Xu PDF

Trans. Amer. Math. Soc. 375 (2022), 3039-3060 Request permission

Abstract:

In this paper we prove that the Cauchy problem of the Muskat equation is wellposed locally in time for any initial data in $\dot C^1(\mathbb {R}^d)\cap L^2(\mathbb {R}^d)$.

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