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Research Article | Open Access

The sharp lifespan for a system of multiple speed wave equations: Radial case

Marvin Koonce, Jason Metcalfe( )
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599–3250, USA
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Abstract

Ohta examined a system of multiple speed wave equations with small initial data and demonstrated a finite time blowup. We show, in the radial case, that the same system exists almost globally with the same lifespan as a lower bound. To do this, we use integrated local energy estimates, r p weighted local energy estimates, the Morawetz estimate that results from using the scaling vector field as a multiplier, and mixed-speed ghost weights.

Keywords

wave equationslocal energy estimatesmultiple speedalmost global existence
CLC number: 35L05, 35L71, 35A01

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Communications in Analysis and Mechanics
Volume 17 Issue 3,
September 2025
Pages 662-682
DOI: 10.3934/cam.2025026

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Cite this article:
Koonce M, Metcalfe J. The sharp lifespan for a system of multiple speed wave equations: Radial case. Communications in Analysis and Mechanics, 2025, 17(3): 662-682. https://doi.org/10.3934/cam.2025026

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Received: 25 January 2025
Revised: 04 June 2025
Accepted: 06 June 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)