Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ^3

Tadahiro Oh; Oana Pocovnicu

doi:10.1016/j.matpur.2015.11.003

Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ^3

Tadahiro Oh
, Oana Pocovnicu

School of Mathematics

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

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3 with random initial data in Hs(ℝ^3)×H^{s−1}(ℝ^3) for s>1/2. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

Original language	English
Pages (from-to)	342-366
Number of pages	25
Journal	Journal de Mathématiques Pures et Appliquées
Volume	105
Issue number	3
Early online date	11 Nov 2015
DOIs	https://doi.org/10.1016/j.matpur.2015.11.003
Publication status	Published - 2 Mar 2016

Keywords / Materials (for Non-textual outputs)

nonlinear wave equation
probabilistic well-posedness
global existence
Wiener randomization

Access to Document

10.1016/j.matpur.2015.11.003

1502.00575v2Accepted author manuscript, 276 KB

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

Cite this

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abstract = "We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3 with random initial data in Hs(ℝ\textasciicircum{}3)×H\textasciicircum{}\{s−1\}(ℝ\textasciicircum{}3) for s>1/2. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions. ",

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AU - Pocovnicu, Oana

PY - 2016/3/2

Y1 - 2016/3/2

N2 - We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3 with random initial data in Hs(ℝ^3)×H^{s−1}(ℝ^3) for s>1/2. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

AB - We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3 with random initial data in Hs(ℝ^3)×H^{s−1}(ℝ^3) for s>1/2. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

KW - nonlinear wave equation

KW - probabilistic well-posedness

KW - global existence

KW - Wiener randomization

U2 - 10.1016/j.matpur.2015.11.003

DO - 10.1016/j.matpur.2015.11.003

M3 - Article

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SP - 342

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JO - Journal de Mathématiques Pures et Appliquées

JF - Journal de Mathématiques Pures et Appliquées

IS - 3

ER -

Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ^3

Abstract

Keywords / Materials (for Non-textual outputs)

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this