Tohoku Mathematical Journal
2017
September
SECOND SERIES VOL. 69, NO. 3

Tohoku Math. J.
69 (2017), 455-481

Title A REMARK ON ALMOST SURE GLOBAL WELL-POSEDNESS OF THE ENERGY-CRITICAL DEFOCUSING NONLINEAR WAVE EQUATIONS IN THE PERIODIC SETTING

Author Tadahiro Oh and Oana Pocovnicu

(Received June 15, 2015)
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.

Mathematics Subject Classification. Primary 35L05; Secondary 35L71.
Key words and phrases. Nonlinear wave equation, probabilistic well-posedness, almost sure global existence, finite speed of propagation.

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