Weak solutions to the Muskat problem with surface tension via optimal transport

DOI10.1007/s00205-020-01579-3zbMath1460.65114arXiv1905.05370OpenAlexW3098643307MaRDI QIDQ2219481

Matthew Jacobs, Alpár Richárd Mészáros, Inwon Christina Kim

Publication date: 20 January 2021

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05370

zbMATH Keywords

weak solutionssurface tensionminimizing movement schemeMuskat problem

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Variational methods applied to PDEs (35A15) Methods involving semicontinuity and convergence; relaxation (49J45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Weak solutions to PDEs (35D30) Other free boundary flows; Hele-Shaw flows (76D27) Numerical solutions to abstract evolution equations (65J08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

Localized mixing zone for Muskat bubbles and turned interfaces, A density-constrained model for chemotaxis, Small scale formations in the incompressible porous media equation, \(\Gamma\) -Convergence of Some Nonlocal Perimeters in Bounded Domains with General Boundary Conditions, A new reformulation of the Muskat problem with surface tension, Density-constrained Chemotaxis and Hele-Shaw flow, Global Regularity for Gravity Unstable Muskat Bubbles, De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions, Mullins-Sekerka as the Wasserstein flow of the perimeter, The Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilities

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