scholarly journals Linear dispersive decay estimates for vortex sheets with surface tension

2009 ◽  
Vol 7 (3) ◽  
pp. 521-547 ◽  
Author(s):  
Daniel Spirn ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Decay Estimates ◽  
Vortex Sheets

scholarly journals Traveling waves from the arclength parameterization: Vortex sheets with surface tension

2013 ◽  
Vol 15 (3) ◽  
pp. 359-380 ◽  
Author(s):  
Benjamin Akers ◽  
David Ambrose ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Traveling Waves ◽  
Vortex Sheets

Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension

2012 ◽  
Vol 55 (1) ◽  
pp. 176-187 ◽  
Author(s):  
Daniel Spirn ◽  
J. Douglas Wright
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Water Wave ◽  
Three Dimensional ◽  
Oscillatory Integral ◽  
Decay Estimates ◽  
Integral Methods ◽  
Flat Interface ◽  
Energy Bounds ◽  
Wave Numbers

AbstractWe consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of t–5/6. This rate is due to competition between surface tension and gravitation at O(1) wave numbers and is connected to the fact that, in the presence of surface tension, there is a so-called “slowest wave”. Additionally, we combine our dispersive estimates with L2 type energy bounds to prove a family of Strichartz estimates.

scholarly journals Well-posedness of 3D vortex sheets with surface tension

2007 ◽  
Vol 5 (2) ◽  
pp. 391-430 ◽  
Author(s):  
David M. Ambrose ◽  
Nader Masmoudi
Keyword(s):  
Surface Tension ◽  
Well Posedness ◽  
Vortex Sheets

scholarly journals Time-Decay Estimates for Linearized Two-Phase Navier–Stokes Equations with Surface Tension and Gravity

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 761
Author(s):  
Hirokazu Saito
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensional Euclidean Space ◽  
Decay Estimates ◽  
Time Decay ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Linearized Equations ◽  
Estimates Of Solutions

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible viscous flow with a sharp interface that is close to the hyperplane xN=0 in the N-dimensional Euclidean space, N≥2. It is well-known that the Rayleigh–Taylor instability occurs when the upper fluid is heavier than the lower one, while this paper assumes that the lower fluid is heavier than the upper one and proves time-decay estimates of Lp-Lq type for the linearized equations. Our approach is based on solution formulas for a resolvent problem associated with the linearized equations.

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