Well-posedness of a diffuse interface model for Hele-Shaw flows

DOI10.1007/s00021-019-0467-9zbMath1435.35297arXiv1903.04457OpenAlexW2996961984WikidataQ126472001 ScholiaQ126472001MaRDI QIDQ2289454

Andrea Giorgini

Publication date: 28 January 2020

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.04457

zbMATH Keywords

uniquenessstrong solutionsDarcy's lawCahn-Hilliard equationlogarithmic potential

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Flows in porous media; filtration; seepage (76S05) Capillarity (surface tension) for incompressible viscous fluids (76D45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Other free boundary flows; Hele-Shaw flows (76D27) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

Related Items (9)

Well-posedness of the two-dimensional Abels-Garcke-Grün model for two-phase flows with unmatched densities ⋮ Weak and stationary solutions to a Cahn-Hilliard-Brinkman model with singular potentials and source terms ⋮ Global well-posedness of a Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential in 2D ⋮ Existence and weak-strong uniqueness of solutions to the Cahn-Hilliard-Navier-Stokes-Darcy system in superposed free flow and porous media ⋮ Nonlocal Cahn-Hilliard-Hele-Shaw systems with singular potential and degenerate mobility ⋮ Global weak solutions to a Navier–Stokes–Cahn–Hilliard system with chemotaxis and singular potential ⋮ On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport ⋮ Well-posedness of a hydrodynamic phase-field system for functionalized membrane-fluid interaction ⋮ On the Existence of Strong Solutions to the Cahn--Hilliard--Darcy System with Mass Source

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