Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$

Tadahiro Oh; Oana Pocovnicu

Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$

Analysis of PDEs 2015-10-22 v2

Authors: Tadahiro Oh , Oana Pocovnicu

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.

Keywords

nonlinear wave equation energy-critical probabilistic well-posedness random initial data quintic nonlinearity global well-posedness

Cite

@article{arxiv.1502.00575,
  title  = {Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$},
  author = {Tadahiro Oh and Oana Pocovnicu},
  journal= {arXiv preprint arXiv:1502.00575},
  year   = {2015}
}

Comments

26 pages. Expanded the introduction. To appear in J. Math. Pures Appl

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