Global well-posedness of 2D non-focusing Schrödinger equations via rigorous modulation approximation

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schrödinger equations (NLS) on R2 with power nonlinearities of arbitrary odd degree. Specifically, the method in this paper applies to those NLS equations having either elliptic signature with a defocusing nonlinearity, or else having an indefinite signature. By rigorously justifying that these equations govern the modulation of wave packet-like solutions to an artificially constructed equation with an advantageous structure, we show that a priori every subcritical inhomogeneous Sobolev norm of the solution increases at most polynomially in time. Global well-posedness follows by a standard application of the subcritical local theory.

Original languageEnglish (US)
Pages (from-to)2251-2299
Number of pages49
JournalJournal of Differential Equations
Volume261
Issue number4
DOIs
StatePublished - Aug 15 2016
Externally publishedYes

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Global Well-posedness
Nonlinear equations
Modulation
Wave packets
Nonlinear Equations
Signature
Approximation
Nonlinearity
Wave Packet
Well-posedness
Cauchy Problem
Odd
Norm
Arbitrary

ASJC Scopus subject areas

  • Analysis

Cite this

Global well-posedness of 2D non-focusing Schrödinger equations via rigorous modulation approximation. / Totz, Nathan.

In: Journal of Differential Equations, Vol. 261, No. 4, 15.08.2016, p. 2251-2299.

Research output: Contribution to journalArticle

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