A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting

Tadahiro Oh; Oana Pocovnicu

doi:doi:10.2748/tmj/1505181626

A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting

Tadahiro Oh, Oana Pocovnicu

School of Mathematics

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

Abstract

In this note, we prove almost sure global well-posedness of the energy-critical defocusing nonlinear wave equation on T^d, d=3,4, and 5, with random initial data below the energy space.

Original language	English
Pages (from-to)	455-481
Number of pages	27
Journal	Tohoku mathematical journal
Volume	69
Issue number	3
DOIs	https://doi.org/doi:10.2748/tmj/1505181626
Publication status	Published - 12 Sep 2017

Keywords

nonlinear wave equation
probabilistic well-posedness
almost sure global existence
finite speed of propagation

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doi:10.2748/tmj/1505181626

1508.00826v1Accepted author manuscript, 435 KB

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

Cite this

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title = "A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting",

abstract = "In this note, we prove almost sure global well-posedness of the energy-critical defocusing nonlinear wave equation on T^d, d=3,4, and 5, with random initial data below the energy space. ",

keywords = "nonlinear wave equation, probabilistic well-posedness, almost sure global existence, finite speed of propagation",

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AU - Pocovnicu, Oana

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AB - In this note, we prove almost sure global well-posedness of the energy-critical defocusing nonlinear wave equation on T^d, d=3,4, and 5, with random initial data below the energy space.

KW - nonlinear wave equation

KW - probabilistic well-posedness

KW - almost sure global existence

KW - finite speed of propagation

U2 - doi:10.2748/tmj/1505181626

DO - doi:10.2748/tmj/1505181626

M3 - Article

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JO - Tohoku mathematical journal

JF - Tohoku mathematical journal

SN - 0040-8735

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A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting

Abstract

Keywords

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this