## Tohoku Mathematical Journal

### 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 $\mathbb{T}^d$, $d = 3, 4,$ and $5$, with random initial data below the energy space.

#### Article information

Source
Tohoku Math. J. (2), Volume 69, Number 3 (2017), 455-481.

Dates
First available in Project Euclid: 12 September 2017

https://projecteuclid.org/euclid.tmj/1505181626

Digital Object Identifier
doi:10.2748/tmj/1505181626

Mathematical Reviews number (MathSciNet)
MR3695994

Zentralblatt MATH identifier
06814879

Subjects
Primary: 35L05: Wave equation
Secondary: 35L71: Semilinear second-order hyperbolic equations

#### Citation

Oh, Tadahiro; Pocovnicu, Oana. A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting. Tohoku Math. J. (2) 69 (2017), no. 3, 455--481. doi:10.2748/tmj/1505181626. https://projecteuclid.org/euclid.tmj/1505181626

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