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2020 Almost-sure scattering for the radial energy-critical nonlinear wave equation in three dimensions
Bjoern Bringmann
Anal. PDE 13(4): 1011-1050 (2020). DOI: 10.2140/apde.2020.13.1011

Abstract

We study the Cauchy problem for the radial energy-critical nonlinear wave equation in three dimensions. Our main result proves almost-sure scattering for radial initial data below the energy space. In order to preserve the spherical symmetry of the initial data, we construct a radial randomization that is based on annular Fourier multipliers. We then use a refined radial Strichartz estimate to prove probabilistic Strichartz estimates for the random linear evolution. The main new ingredient in the analysis of the nonlinear evolution is an interaction flux estimate between the linear and nonlinear components of the solution. We then control the energy of the nonlinear component by a triple bootstrap argument involving the energy, the Morawetz term, and the interaction flux estimate.

Citation

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Bjoern Bringmann. "Almost-sure scattering for the radial energy-critical nonlinear wave equation in three dimensions." Anal. PDE 13 (4) 1011 - 1050, 2020. https://doi.org/10.2140/apde.2020.13.1011

Information

Received: 24 April 2018; Accepted: 18 April 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07221195
MathSciNet: MR4109898
Digital Object Identifier: 10.2140/apde.2020.13.1011

Subjects:
Primary: 35L05, 35L15, 35L71

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2020
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