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Two dimensional water waves in holomorphic coordinates

PDE and Applied Math Seminar

Speaker: Mihaela Ifrim, McMaster University
Location: 1147 MSB
Start time: Tue, Nov 19 2013, 3:10PM

This talk is concerned with the infinite bottom water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive equation, we establish two results: (i) local well-posedness in Sobolev spaces, and (ii) almost global solutions for small localized data. Neither of these results are new; they have been recently obtained by Alazard-Burq-Zuily, respectively by Wu using different coordinates and methods. Instead, our goal is to improve the understanding of this problem by providing a single setting for both problems and by proving sharper versions of the above results as well as by presenting new simpler proofs. This talk is self-contained. (Joint work with Daniel Tataru and John Hunter)