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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 |
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Vol. 17 (2024), No. 1, 1–9
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Abstract |
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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. |
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Keywords
semilinear wave equations, null condition, global
existence, local energy estimate
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Mathematical Subject Classification
Primary: 35L05, 35L71
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Milestones
Received: 27 January 2021
Accepted: 7 January 2023
Published: 15 March 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Michael Facci | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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| Alex McEntarrfer | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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| Jason Metcalfe | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
