Nonlinear Schrödinger equation and frequency saturation

DOI10.2140/APDE.2012.5.1157zbMATH Open1264.35208arXiv1112.2594OpenAlexW3100294248MaRDI QIDQ1951751

Rémi Carles

Publication date: 24 May 2013

Published in: Analysis \& PDE (Search for Journal in Brave)

Abstract: We propose an approach that permits to avoid instability phenomena for the nonlinear Schrodinger 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.

Full work available at URL: https://arxiv.org/abs/1112.2594

zbMATH Keywords

well-posednessapproximationnonlinear Schrödinger equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

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