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Science China Mathematics

, Volume 62, Issue 6, pp 1087–1100 | Cite as

A survey of the Szegő equation

  • Patrick GérardEmail author
  • Sandrine Grellier
Reviews
  • 34 Downloads

Abstract

We survey the main properties of the cubic Szegő equation from the PDE viewpoint, emphasising global existence of smooth solutions, analytic regularity, growth of high Sobolev norms and the effects of weak damping.

Keywords

cubic Szegő equation integrable system Hankel operator spectral analysis analytic regularity wave turbulence 

MSC(2010)

35B15 35B65 47B35 37K15 

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Copyright information

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

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’OrsayUniversité Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance
  2. 2.Institut Denis Poisson-Université d’Orléans/Université de ToursOrléansFrance

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