Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$
By Tadahiro Oh, Oana Pocovnicu. 2015
65 citations recorded by the source corpus.
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.
Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/40f0714049d5696d7f5d7087fac8fcbf0e91c0b9
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In Control and Systems Engineering
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data (2017, background): “possesses almost surely much better integrability properties. In many cases this approach has yielded probabilistic local and global existence results for super-critical initial data, see for example [49, 29, 3, 4, 35, 32, 30, 8], as well as Remark 1.1 for further discussion. We take this direct app”