Probabilistic global well-posedness of the energy-critical defocusing\n quintic nonlinear wave equation on \ℝ³

2015/02/02 by Tadahiro Oh, Oana Pocovnicu, Oh, Tadahiro +1 · 1 citation
Mathematics · Physics and Astronomy · #35L05 #35L15 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1502.00575

openalex publication_date 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing\nquintic nonlinear wave equation on \ℝ³ with random initial data in \nH^s(\ℝ³) \× H^s-1(\ℝ³) for s > frac 12. The main\nnew ingredient is a uniform probabilistic energy bound for approximating random\nsolutions.\n

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