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

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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 equations / local energy estimates / multiple speed / almost global existence

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