Spitalfields 1: Guido Schneider speaks on validity and non-validity of NLS

NLS_profile_newThe first talk of the Spitalfields Day was by Guido Schneider.  He presented an introduction to the approximation scheme used to prove validity in finite depth.  The full solution of the irrotational Euler equations was expressed in terms of an NLS component and a remainder.  Then a PDE was derived for the remainder term, and then analyzed.  Key tools were normal form transformations, energy estimates, and the Cauchy-Kowalevskaya theorem.  The non-validity result was for water waves with surface tension and spatially periodic boundaries.  There a 3-wave resonance was shown to nullify validity of NLS.  Some discussion of validity of the 3-wave interaction was also presented, based on the preprint here.  A preprint on the proof of validity for NLS can be found here.

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