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

Tadahiro Oh, Oana Pocovnicu

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)
34 Downloads (Pure)

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.
Original languageEnglish
Pages (from-to)342–366
Number of pages15
JournalJournal de Mathématiques Pures et Appliquées
Volume105
Issue number3
Early online date11 Nov 2015
DOIs
Publication statusPublished - Mar 2016

Keywords

  • Partial differential equations
  • Probability theory and stochastic processes

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