Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting

DOI10.2140/paa.2024.6.187arXiv2203.00075MaRDI QIDQ6123306

Juan J. L. Velazquez, Christina Lienstromberg

Publication date: 4 March 2024

Published in: Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.00075

zbMATH Keywords

non-Newtonian fluidpower-law fluidlong-time asymptoticsweak-solutionpolynomial stabilitythin-film equationregularity estimatesTaylor-Couette flowdegenerate-parabolic equation

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20) Degenerate parabolic equations (35K65)

Cites Work

• Thin-film approximations of the two-phase Stokes problem
• Smooth zero-contact-angle solutions to a thin-film equation around the steady state
• A justification for the thin film approximation of Stokes flow with surface tension
• Existence results for doubly nonlinear higher order parabolic equations on unbounded domains
• Compact sets in the space \(L^ p(0,T;B)\)
• Fundamentals of two-fluid dynamics. Part I: Mathematical theory and applications
• Two generalizations of the thin film equation
• Doubly nonlinear thin-film equations in one space dimension
• Analysis of a thin film approximation for two-fluid Taylor-Couette flows
• Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid
• Local strong solutions to a quasilinear degenerate fourth-order thin-film equation
• Couette flow of two fluids between concentric cylinders
• Hydrodynamic Stability
• Shear-thinning liquid films: macroscopic and asymptotic behaviour by quasi-self-similar solutions
• Viscous Flow
• Contact-line motion of shear-thinning liquids
• Self-Similarity in a Thin Film Muskat Problem
• The Spreading of Power-Law Fluids
• Flow regimes in model viscoelastic fluids in a circular couette system with independently rotating cylinders
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