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

Oana  Pocovnicu; Yuzhao Wang

doi:10.1016/j.crma.2018.04.009

An L^p-theory for almost sure local well-posedness of the nonlinear Schrödinger equations

Oana Pocovnicu, Yuzhao Wang

Mathematics

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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 language	English
Pages (from-to)	637-643
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	6
Early online date	25 Apr 2018
DOIs	https://doi.org/10.1016/j.crma.2018.04.009
Publication status	Published - Jun 2018

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https://doi.org/10.1016/j.crma.2018.04.009
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title = "An Lp-theory for almost sure local well-posedness of the nonlinear Schr{\"o}dinger equations",

abstract = "We consider the nonlinear Schr{\"o}dinger 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.",

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AB - 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.

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DO - 10.1016/j.crma.2018.04.009

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

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An L^p-theory for almost sure local well-posedness of the nonlinear Schrödinger equations