The Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability

DOI10.1080/03605302.2012.699498zbMath1294.76143arXiv1109.5657OpenAlexW2049657837MaRDI QIDQ4902756

Yanjin Wang, Ian Tice

Publication date: 17 January 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5657

zbMATH Keywords

Navier-Stokes equationsfree boundary problemsurface tension

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear effects in hydrodynamic stability (76E30) 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) Waves for incompressible viscous fluids (76D33) Other free boundary flows; Hele-Shaw flows (76D27)

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Cites Work

• Unnamed Item
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• Dynamics near unstable, interfacial fluids
• On the dynamical Rayleigh-Taylor instability
• Surface Waves
• Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability
• On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations
• Compressible, inviscid Rayleigh-Taylor instability
• Linear Rayleigh–Taylor Instability for Viscous, Compressible Fluids
• Commutator estimates and the euler and navier-stokes equations
• The initial value problem for the navier-stokes equations with a free surface
• SOLVABILITY OF A PROBLEM ON THE MOTION OF A VISCOUS INCOMPRESSIBLE FLUID BOUNDED BY A FREE SURFACE
• Free Boundary Fluid Systems in a Semigroup Approach and Oscillatory Behavior
• Ill-posedness of the rayleigh-taylor and helmholtz problems for incompressible fluids
• Instability of periodic BGK equilibria
• The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I

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