On the Cauchy problem for the Muskat equation with non-Lipschitz initial data

DOI10.1080/03605302.2021.1928700zbMath1477.35151arXiv2009.04343OpenAlexW3169495828MaRDI QIDQ5012787

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Publication date: 25 November 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.04343

zbMATH Keywords

Darcyfree boundary flowcritical Cauchy problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Other free boundary flows; Hele-Shaw flows (76D27) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

On the dynamics of the roots of polynomials under differentiation ⋮ Localized mixing zone for Muskat bubbles and turned interfaces ⋮ The Muskat problem with 𝐶¹ data ⋮ Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space ⋮ Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data ⋮ The Peskin Problem with \({\boldsymbol{\dot B^1_{\infty,\infty }}}\) Initial Data ⋮ Endpoint Sobolev theory for the Muskat equation ⋮ Critical local well‐posedness for the fully nonlinear Peskin problem ⋮ Regularity of solutions to the Muskat equation ⋮ Rigidity of acute angled corners for one phase Muskat interfaces ⋮ Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem ⋮ Self-similar solutions for the Muskat equation

Cites Work

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