Endpoint Sobolev theory for the Muskat equation

DOI10.1007/s00220-022-04514-7OpenAlexW3093369816MaRDI QIDQ2684869

Yanyan Li

Publication date: 17 February 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.06915

zbMATH Keywords

Cauchy problemfree surfaceTriebel-Lizorkin spaceexistence resultMuskat equationfractional porous media equationnull-type structureweighted fractional Laplacian

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Fractional derivatives and integrals (26A33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Other free boundary flows; Hele-Shaw flows (76D27) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Liquid-liquid two component flows (76T06)

Related Items (4)

A note on the dissipation for the general Muskat problem ⋮ Global well‐posedness for the one‐phase Muskat problem ⋮ The Peskin Problem with \({\boldsymbol{\dot B^1_{\infty,\infty }}}\) Initial Data ⋮ Existence of weak solutions for porous medium equation with a divergence type of drift term in a bounded domain

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