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

作者：Pocovnicu Oana^*

来源：Journal of the European Mathematical Society, 2017, 19(8): 2521-2575.

DOI：10.4171/JEMS/723

• Nonlinear wave equations
• almost sure well-posedness
• probabilistic continuous dependence
• Wiener decomposition

We consider the energy-critical defocusing nonlinear wave equation (NLW) on R-d, d = 4; 5. We prove almost sure global existence and uniqueness for NLWwith rough random initial data in H-s. (R-d) x Hs(-1) (R-d) with 0 < s <= 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 on the initial data (in the sense proposed by Burq and Tzvetkov [19]).

• 出版日期2017