Geodesic
Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb R^d$, $d=4$ and $5$
Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2521-2575 Cet article a éte moissonné depuis la source EMS Press

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We consider the energy-critical defocusing nonlinear wave equation (NLW) on Rd, d=4 and 5. We prove almost sure global existence and uniqueness for NLW with rough random initial data in Hs(Rd)×Hs−1(Rd), with 0≤1 if d=4, and 0≤s≤1 if d=5. The randomization we consider is naturally associated with the Wiener decomposition and with modulation spaces. The proof is based on a probabilistic perturbation theory. Under some additional assumptions, for d=4, we also prove the probabilistic continuous dependence of the flow with respect to the initial data (in the sense proposed by Burq and Tzvetkov).
DOI : 10.4171/jems/723
Classification : 35-XX
Keywords: Nonlinear wave equations, almost sure well-posedness, probabilistic continuous dependence, Wiener decomposition 
@article{JEMS_2017_19_8_a7,
     author = {Oana Pocovnicu},
     title = {Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb R^d$, $d=4$ and $5$},
     journal = {Journal of the European Mathematical Society},
     pages = {2521--2575},
     year = {2017},
     volume = {19},
     number = {8},
     doi = {10.4171/jems/723},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/723/}
}
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Oana Pocovnicu. Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb R^d$, $d=4$ and $5$. Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2521-2575. doi: 10.4171/jems/723

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