Analysis & PDE

  • Anal. PDE
  • Volume 5, Number 5 (2012), 1157-1173.

Nonlinear Schrödinger equation and frequency saturation

Rémi Carles

Full-text: Open access

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.

Article information

Source
Anal. PDE, Volume 5, Number 5 (2012), 1157-1173.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731268

Digital Object Identifier
doi:10.2140/apde.2012.5.1157

Mathematical Reviews number (MathSciNet)
MR3022853

Zentralblatt MATH identifier
1264.35208

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35A01: Existence problems: global existence, local existence, non-existence 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B45: A priori estimates 35B65: Smoothness and regularity of solutions

Keywords
nonlinear Schrödinger equation well-posedness approximation

Citation

Carles, Rémi. Nonlinear Schrödinger equation and frequency saturation. Anal. PDE 5 (2012), no. 5, 1157--1173. doi:10.2140/apde.2012.5.1157. https://projecteuclid.org/euclid.apde/1513731268


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