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arXiv · 2501.18806

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

Marvin Koonce·Jason Metcalfe
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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 estimate, $r^p$ weighted local energy estimates, the Morawetz estimate that results from using the scaling vector field as a multiplier, and mixed speed ghost weights.

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Marvin Koonce, Jason Metcalfe. 2025-01-30. The sharp lifespan for a system of multiple speed wave equations: Radial case. https://arxiv.org/abs/2501.18806

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