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2012 Nonlinear Schrödinger equation and frequency saturation
Rémi Carles
Anal. PDE 5(5): 1157-1173 (2012). DOI: 10.2140/apde.2012.5.1157

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.

Citation

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Rémi Carles. "Nonlinear Schrödinger equation and frequency saturation." Anal. PDE 5 (5) 1157 - 1173, 2012. https://doi.org/10.2140/apde.2012.5.1157

Information

Received: 8 December 2011; Revised: 15 February 2012; Accepted: 20 March 2012; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1264.35208
MathSciNet: MR3022853
Digital Object Identifier: 10.2140/apde.2012.5.1157

Subjects:
Primary: 35Q55
Secondary: 35A01, 35B30, 35B45, 35B65

Rights: Copyright © 2012 Mathematical Sciences Publishers

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