Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ^3

Tadahiro Oh, Oana Pocovnicu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ3 with random initial data in Hs(ℝ^3)×H^{s−1}(ℝ^3) for s>1/2. The main new ingredient is a uniform probabilistic energy bound for approximating random solutions.
Original languageEnglish
Pages (from-to)342-366
Number of pages25
JournalJournal de Mathématiques Pures et Appliquées
Volume105
Issue number3
Early online date11 Nov 2015
DOIs
Publication statusPublished - 2 Mar 2016

Keywords

  • nonlinear wave equation
  • probabilistic well-posedness
  • global existence
  • Wiener randomization

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