Vol. 12, No. 4, 2019

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ISSN: 1948-206X (e-only)
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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 B1,12 × B1,11. This space of functions is a scale-invariant subspace of 12 ×12.

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