Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

Dodson, Benjamin

doi:10.2140/apde.2019.12.1023

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Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

Benjamin Dodson

Vol. 12 (2019), No. 4, 1023–1048

DOI: 10.2140/apde.2019.12.1023

Abstract

We prove that the cubic wave equation is globally well-posed and scattering for radial initial data lying in $B_{1, 1}^{2} \times B_{1, 1}^{1}$ . This space of functions is a scale-invariant subspace of $Ḣ^{1 ∕ 2} \times Ḣ^{- 1 ∕ 2}$ .

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Keywords

defocusing, nonlinear wave equation, scattering, global well-posedness

Mathematical Subject Classification 2010

Primary: 35L05, 35B40

Milestones

Received: 10 July 2017

Revised: 2 April 2018

Accepted: 5 July 2018

Published: 20 October 2018

Authors

Benjamin Dodson
Department of Mathematics Johns Hopkins University Baltimore, MD United States

Vol. 12, No. 4, 2019