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The NLS approximation for two dimensional deep gravity waves

  • Mihaela Ifrim
  • Daniel TataruEmail author
Articles
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Abstract

This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet data, and to show that this is well approximated by the cubic nonlinear Schrödinger equation (NLS) on the natural cubic time scale.

Keywords

water waves gravity waves normal forms NLS approximation 

MSC(2010)

76B15 35Q31 

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Notes

Acknowledgements

The first author was supported by a Clare Boothe Luce Professorship. The second author was supported by the National Science Foundation of USA (Grant No. DMS-1800294) and a Simons Investigator grant from the Simons Foundation.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Wisconsin at MadisonMadisonUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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