Vol. 5, No. 5, 2012

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Nonlinear Schrödinger equation and frequency saturation

Rémi Carles

Vol. 5 (2012), No. 5, 1157–1173
Abstract

We propose an approach that permits to avoid instability phenomena for the nonlinear Schrödinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity. The error between the exact solution and its approximation can be measured according to the regularity of the exact solution, with different accuracy according to the cases considered.

Keywords
nonlinear Schrödinger equation, well-posedness, approximation
Mathematical Subject Classification 2010
Primary: 35Q55
Secondary: 35A01, 35B30, 35B45, 35B65
Milestones
Received: 8 December 2011
Revised: 15 February 2012
Accepted: 20 March 2012
Published: 29 December 2012
Authors
Rémi Carles
CNRS & Université Montpellier 2
UMR 5149, Mathématiques, CC051
Place Eugène Bataillon
34095 Montpellier
France