Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝd , d = 4 and 5

Oana Pocovnicu

doi:10.4171/JEMS/723

Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝ^d , d = 4 and 5

Oana Pocovnicu

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

47 Citations (Scopus)

Abstract

We consider the energy-critical defocusing nonlinear wave equation (NLW) on $\mathbb{R}^d$, $d=4$ and $5$. We prove almost sure global existence and uniqueness for NLW with rough random initial data in $H^s(\mathbb{R}^d)\times H^{s-1}(\mathbb{R}^d)$, with $0

Original language	English
Pages (from-to)	2521-2575
Number of pages	55
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	8
DOIs	https://doi.org/10.4171/JEMS/723
Publication status	Published - 2017

Keywords

Partial differential equations
Probability theory and stochastic processes

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10.4171/JEMS/723

http://arxiv.org/pdf/1406.1782v3

Cite this

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title = "Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝd , d = 4 and 5",

abstract = "We consider the energy-critical defocusing nonlinear wave equation (NLW) on $\mathbb{R}^d$, $d=4$ and $5$. We prove almost sure global existence and uniqueness for NLW with rough random initial data in $H^s(\mathbb{R}^d)\times H^{s-1}(\mathbb{R}^d)$, with $0",

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AB - We consider the energy-critical defocusing nonlinear wave equation (NLW) on $\mathbb{R}^d$, $d=4$ and $5$. We prove almost sure global existence and uniqueness for NLW with rough random initial data in $H^s(\mathbb{R}^d)\times H^{s-1}(\mathbb{R}^d)$, with $0

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KW - Probability theory and stochastic processes

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DO - 10.4171/JEMS/723

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JF - Journal of the European Mathematical Society

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Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝ^d , d = 4 and 5

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Oana Pocovnicu

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Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝd , d = 4 and 5

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Keywords

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Oana Pocovnicu

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Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on ℝ^d , d = 4 and 5