Vol. 13, No. 7, 2020

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Scattering for defocusing energy subcritical nonlinear wave equations

Benjamin Dodson, Andrew Lawrie, Dana Mendelson and Jason Murphy

Vol. 13 (2020), No. 7, 1995–2090
Abstract

We consider the Cauchy problem for the defocusing power-type nonlinear wave equation in (1+ 3)-dimensions for energy subcritical powers p in the superconformal range 3 < p < 5. We prove that any solution is global-in-time and scatters to free waves in both time directions as long as its critical Sobolev norm stays bounded on the maximal interval of existence.

Keywords
nonlinear waves, scattering
Mathematical Subject Classification 2010
Primary: 35L71
Milestones
Received: 16 October 2018
Accepted: 6 September 2019
Published: 10 November 2020
Authors
Benjamin Dodson
Department of Mathematics
Johns Hopkins University
Baltimore, MD
United States
Andrew Lawrie
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Dana Mendelson
Department of Mathematics
University of Chicago
Chicago, IL
United States
Jason Murphy
Department of Mathematics and Statistics
Missouri University of Science and Technology
Rolla, MO
United States