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An $r^p$-weighted local energy approach to global existence for null form semilinear wave equations

Michael Facci, Alex McEntarrfer and Jason Metcalfe

Vol. 17 (2024), No. 1, 1–9
Abstract

We revisit the proof of small-data global existence for semilinear wave equations that satisfy a null condition. This new approach relies on a weighted local energy estimate that is akin to those of Dafermos and Rodnianski. Using weighted Sobolev estimates to obtain spatial decay and arguing in the spirit of the work of Keel, Smith, and Sogge, we are able to obtain global existence while only relying on translational and (spatial) rotational symmetries.

Keywords
semilinear wave equations, null condition, global existence, local energy estimate
Mathematical Subject Classification
Primary: 35L05, 35L71
Milestones
Received: 27 January 2021
Accepted: 7 January 2023
Published: 15 March 2024

Communicated by Kenneth S. Berenhaut
Authors
Michael Facci
Department of Mathematics
University of North Carolina
Chapel Hill, NC
United States
Alex McEntarrfer
Department of Mathematics
University of North Carolina
Chapel Hill, NC
United States
Jason Metcalfe
Department of Mathematics
University of North Carolina
Chapel Hill, NC
United States