Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R3

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 R³

Tadahiro Oh, Oana Pocovnicu

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Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. 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	15
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 - Mar 2016

Keywords

Partial differential equations
Probability theory and stochastic processes

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10.1016/j.matpur.2015.11.003

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title = "Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R3",

abstract = "We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on \$\textbackslash{}mathbb\{R\}\textasciicircum{}3\$ with random initial data in \$ H\textasciicircum{}s(\textbackslash{}mathbb\{R\}\textasciicircum{}3) \textbackslash{}times H\textasciicircum{}\{s-1\}(\textbackslash{}mathbb\{R\}\textasciicircum{}3)\$ for \$s > \textbackslash{}frac 12\$. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.",

keywords = "Partial differential equations, Probability theory and stochastic processes",

author = "Tadahiro Oh and Oana Pocovnicu",

year = "2016",

month = mar,

doi = "10.1016/j.matpur.2015.11.003",

language = "English",

volume = "105",

pages = "342–366",

journal = "Journal de Math{\'e}matiques Pures et Appliqu{\'e}es",

issn = "0021-7824",

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T1 - Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R3

AU - Oh, Tadahiro

AU - Pocovnicu, Oana

PY - 2016/3

Y1 - 2016/3

N2 - We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. 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 $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.

KW - Partial differential equations

KW - Probability theory and stochastic processes

UR - http://arxiv.org/abs/1502.00575

U2 - 10.1016/j.matpur.2015.11.003

DO - 10.1016/j.matpur.2015.11.003

M3 - Article

SN - 0021-7824

VL - 105

SP - 342

EP - 366

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 R³

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Oana Pocovnicu

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Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R3

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Oana Pocovnicu

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Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on R³