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

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

143 Downloads (Pure)

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

Access to Document

10.1016/j.crma.2018.04.009Licence: None: All rights reserved

Pocovnicu_et_al_An_Lp-theory_for_almost_Comptes_Rendus_Mathematique_2018
https://doi.org/10.1016/j.crma.2018.04.009
Accepted author manuscript, 330 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

https://www.sciencedirect.com/science/article/pii/S1631073X18301237Licence: None: All rights reserved

Cite this

@article{985df770f98540ffb14d3095924f3345,

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.",

author = "Oana Pocovnicu and Yuzhao Wang",

year = "2018",

month = jun,

doi = "10.1016/j.crma.2018.04.009",

language = "English",

volume = "356",

pages = "637--643",

journal = "Comptes Rendus Mathematique",

issn = "1631-073X",

publisher = "Elsevier Masson",

number = "6",

}

TY - JOUR

T1 - An Lp-theory for almost sure local well-posedness of the nonlinear Schrödinger equations

AU - Pocovnicu, Oana

AU - Wang, Yuzhao

PY - 2018/6

Y1 - 2018/6

N2 - 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.

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.

U2 - 10.1016/j.crma.2018.04.009

DO - 10.1016/j.crma.2018.04.009

M3 - Article

SN - 1631-073X

VL - 356

SP - 637

EP - 643

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 6

ER -

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

Abstract

Access to Document

Fingerprint

Cite this

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