Vol. 8, No. 2, 2015

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Scattering for the radial 3D cubic wave equation

Benjamin Dodson and Andrew Lawrie

Vol. 8 (2015), No. 2, 467–497
Abstract

Consider the Cauchy problem for the radial cubic wave equation in 1 + 3 dimensions with either the focusing or defocusing sign. This problem is critical in 12 ×12(3) and subcritical with respect to the conserved energy. Here we prove that if the critical norm of a solution remains bounded on the maximal time interval of existence, then the solution must in fact be global in time and must scatter to free waves as t ±.

Keywords
scattering, concentration compactness, double Duhamel
Mathematical Subject Classification 2010
Primary: 35L05
Milestones
Received: 20 May 2014
Revised: 12 October 2014
Accepted: 26 November 2014
Published: 10 May 2015
Authors
Benjamin Dodson
Department of Mathematics
Johns Hopkins University
404 Krieger Hall
3400 N. Charles Street
Baltimore, CA 21218
United States
Andrew Lawrie
Department of Mathematics
University of California, Berkeley
970 Evans Hall #3840
Berkeley, CA 94720
United States