Local Well Posedness of the Near-Equilibrium Contact Line Problem in 2-Dimensional Stokes Flow

DOI10.1137/16M1095238zbMath1365.35232arXiv1609.07085OpenAlexW2598905922MaRDI QIDQ5737780

Ian Tice, Yun Rui Zheng

Publication date: 30 May 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.07085

zbMATH Keywords

Stokes flowincompressible viscous fluidsfree boundary problemscapillarity

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Capillarity (surface tension) for incompressible viscous fluids (76D45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35) Statistical solutions of Navier-Stokes and related equations (76D06) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

Solvability of a moving contact-line problem with interface formation for an incompressible viscous fluid ⋮ Stability of contact lines in fluids: 2D Stokes flow ⋮ Dynamics and stability of sessile drops with contact points ⋮ A priori estimates for water waves with emerging bottom ⋮ The Viscous Surface Wave Problem with Generalized Surface Energies ⋮ On a fluid-structure interaction problem for plaque growth: cylindrical domain ⋮ Local well-posedness of incompressible viscous fluids in bounded cylinders with \(90^\circ \)-contact angle

Cites Work

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• Local well-posedness of the viscous surface wave problem without surface tension
• Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
• Stability of contact lines in fluids: 2D Stokes flow
• Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
• Almost exponential decay of periodic viscous surface waves without surface tension
• Stability in the Stefan Problem with Surface Tension (I)
• On Korn's second inequality

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