Stable and unstable singularities in the unforced Hele-Shaw cell

DOI10.1063/1.868915zbMath1087.76028OpenAlexW2055388805MaRDI QIDQ4426411

Michael P. Brenner, Robert Almgren, Andrea L. Bertozzi

Publication date: 1996

Published in: Physics of Fluids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.868915

zbMATH Keywords

lubrication model

Mathematics Subject Classification ID

Lubrication theory (76D08) Hydrodynamic stability (76E99) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (16)

Arrested bubble rise in a narrow tube ⋮ A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem ⋮ Singular limit of an energy minimizer arising from dewetting thin film model with Van der waal, born repulsion and surface tension forces ⋮ Similarity solutions for van der Waals rupture of a thin film on a solid substrate ⋮ Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse ⋮ Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration ⋮ Modeling pinchoff and reconnection in a Hele-Shaw cell. II. Analysis and simulation in the nonlinear regime ⋮ A fully coupled mixed finite element method for surfactants spreading on thin liquid films ⋮ On singularity formation in a Hele-Shaw model ⋮ Algebraic properties of some quadratic dynamical systems ⋮ Boundary integral methods for multicomponent fluids and multiphase materials. ⋮ The long-time motion of vortex sheets with surface tension ⋮ Instabilities and singularities in Hele–Shaw flow ⋮ A dynamical systems approach for the contact-line singularity in thin-film flows ⋮ Nonlinear dynamics and breakup of free-surface flows ⋮ How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations?

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• Singularity formation in Hele–Shaw bubbles
• Symmetric Singularity Formation in Lubrication-Type Equations for Interface Motion
• Global solutions for small data to the Hele-Shaw problem

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