Validity of hyperbolic NLS for water waves in three dimensions

nlsOn Thursday afternoon, 24 July, Nathan Totz, gave a talk on validity results for the NLS equation in 2D and 3D.  The first half of the talk reviewed the validity proof of NLS in deep water, co-authored with Sijue Wu. It was a summary of their 2012 paper which can be found here.  The second half discussed the validity of the hyperbolic NLS in deep water.  The methodology included the use of Lagrangian coordinates, Clifford analysis, quaternionic representation of the Lagrangian position coordinates, normal form transformations, and energy estimates, leading to results in Sobolev spaces, including a priori bounds on the difference between the true and approximate solutions.  In both the 2D and 3D case surface tension was neglected.  A preprint by Totz on the 3D case can be found here. A video of the talk is available here.

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