Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

DOI10.1007/s00033-018-0926-9zbMath1392.35212arXiv1708.02141OpenAlexW2744430731MaRDI QIDQ1635926

Ian Tice

Publication date: 1 June 2018

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.02141

zbMATH Keywords

shear flowsfree boundary problemsviscous surface waves

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations (35Q30) Interfacial stability and instability in hydrodynamic stability (76E17) Capillarity (surface tension) for incompressible viscous fluids (76D45) Free boundary problems for PDEs (35R35) Parallel shear flows in hydrodynamic stability (76E05)

Related Items (4)

Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations ⋮ Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension ⋮ Traveling wave solutions to the inclined or periodic free boundary incompressible Navier-Stokes equations ⋮ The nonlinear stability regime of the viscous Faraday wave problem

Cites Work

• Unnamed Item
• The compressible viscous surface-internal wave problem: stability and vanishing surface tension limit
• Viscous incompressible free-surface flow down an inclined perturbed plane
• On a linearized system arising in the study of viscous surface flow down an inclined plane
• Large-time regularity of viscous surface waves
• Uniform estimates for the flow of a viscous incompressible fluid down an inclined plane in the thin film regime
• Decaying solution of a Navier-Stokes flow without surface tension
• A mathematical theory for viscous, free-surface flows over a perturbed plane
• Hopf bifurcation in viscous incompressible flow down an inclined plane
• Large-time existence of surface waves in incompressible viscous fluids with or without surface tension
• On stability of a capillary liquid down an inclined plane
• Almost exponential decay of periodic viscous surface waves without surface tension
• Stationary free surface viscous flows without surface tension in three dimensions.
• Zero surface tension limit of viscous surface waves
• Decay of viscous surface waves without surface tension in horizontally infinite domains
• Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients
• Global in time behavior of viscous surface waves: horizontally periodic motion
• Well-Posedness and Decay of the Viscous Surface Wave
• The initial value problem for the navier-stokes equations with a free surface
• On stability of liquid flow down an inclined plane
• Asymptotische Integration der Störungsdifferentialgleichung ebener laminarer Strömungen bei hohen Reynoldsschen Zahlen
• On the Stability of Two-Dimensional Parallel Flows
• Spectral instability of general symmetric shear flows in a two-dimensional channel

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