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

2014/06/06 by Oana Pocovnicu, Pocovnicu, Oana · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1406.1782

openalex publication_date 2014/06/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We consider the energy-critical defocusing nonlinear wave equation (NLW) on\n\ℝ^d, d=4 and 5. We prove almost sure global existence and\nuniqueness for NLW with rough random initial data in H^s(\ℝ^d)\×\nH^s-1(\ℝ^d), with 0< s\≤ 1 if d=4, and 0\≤ s\≤ 1 if\nd=5. The randomization we consider is naturally associated with the Wiener\ndecomposition and with modulation spaces. The proof is based on a probabilistic\nperturbation theory. Under some additional assumptions, for d=4, we also\nprove the probabilistic continuous dependence of the flow with respect to the\ninitial data (in the sense proposed by Burq and Tzvetkov).\n

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