Vol. 6, No. 3, 2013

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Bilinear dispersive estimates via space-time resonances, I: The one-dimensional case

Frédéric Bernicot and Pierre Germain

Vol. 6 (2013), No. 3, 687–722
Abstract

We prove new bilinear dispersive estimates. They are obtained and described via a bilinear time-frequency analysis following the space-time resonances method, introduced by Masmoudi, Shatah, and the second author. They allow us to understand the large time behavior of solutions of quadratic dispersive equations.

Keywords
bilinear dispersive estimates , space-time resonances , Strichartz inequalities
Mathematical Subject Classification 2010
Primary: 37L50, 42B20
Milestones
Received: 21 October 2011
Revised: 25 April 2012
Accepted: 26 June 2012
Published: 11 July 2013
Authors
Frédéric Bernicot
Laboratoire de mathématiques Paul Painlevé
CNRS, Université Lille 1
59655 Villeneuve d’Ascq Cedex
France
Laboratoire Jean Leray
CNRS, Universite de Nantes
2, rue de la Houssiniere
44322 Nantes Cedex 3
France
http://www.math.sciences.univ-nantes.fr/~bernicot/
Pierre Germain
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, New York 10012-1185
United States
http://cims.nyu.edu/~pgermain/