An Lp-theory for almost sure local well-posedness of the nonlinear Schrödinger equations

Oana Pocovnicu, Yuzhao Wang

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Abstract

We consider the nonlinear Schrödinger equations (NLS) on with random and rough initial data. By working in the framework of spaces, , we prove almost sure local well-posedness for rougher initial data than those considered in the existing literature. The main ingredient of the proof is the dispersive estimate.
Original languageEnglish
Pages (from-to)637-643
Number of pages7
JournalComptes Rendus Mathématique
Volume356
Issue number6
Early online date25 Apr 2018
DOIs
Publication statusPublished - Jun 2018

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