scholarly journals Strichartz Estimates for the Water-Wave Problem with Surface Tension

2010 ◽  
Vol 35 (12) ◽  
pp. 2195-2252 ◽  
Author(s):  
Hans Christianson ◽  
Vera Mikyoung Hur ◽  
Gigliola Staffilani
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Strichartz Estimates ◽  
Wave Problem ◽  
Water Wave Problem

The NLS and FWI approximation make wrong predictions for the water wave problem in case of small surface tension

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 747-748
Author(s):  
Danish Ali Sunny ◽  
Guido Schneider ◽  
Dominik Zimmermann
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Small Surface

scholarly journals Local smoothing effects for the water-wave problem with surface tension

2009 ◽  
Vol 347 (3-4) ◽  
pp. 159-162 ◽  
Author(s):  
Hans Christianson ◽  
Vera Mikyoung Hur ◽  
Gigliola Staffilani
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Local Smoothing ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Smoothing Effects

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

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