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

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Abstract

We consider the energy-critical defocusing nonlinear wave equation (NLW) on $\mathbb{R}^d$, $d=4$ and $5$. We prove almost sure global existence and uniqueness for NLW with rough random initial data in $H^s(\mathbb{R}^d)\times H^{s-1}(\mathbb{R}^d)$, with $0
Original languageEnglish
Pages (from-to)2521-2575
Number of pages55
JournalJournal of the European Mathematical Society
Volume19
Issue number8
DOIs
Publication statusPublished - 2017

Keywords

  • Partial differential equations
  • Probability theory and stochastic processes

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