scholarly journals Validity of the Nonlinear Schrödinger Approximation for the Two-Dimensional Water Wave Problem With and Without Surface Tension in the Arc Length Formulation

2020 ◽  
Author(s):  
Wolf-Patrick Düll
Keyword(s):  
Surface Tension ◽  
Water Wave ◽  
Two Dimensional ◽  
Arc Length ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Nonlinear Schrödinger

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 example of non-uniqueness in the two-dimensional linear water wave problem

1996 ◽  
Vol 315 ◽  
pp. 257-266 ◽  
Author(s):  
M. McIver
Keyword(s):  
Free Surface ◽  
Numerical Calculation ◽  
Water Wave ◽  
Two Dimensional ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Source Point ◽  
The Waves

An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.

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
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