Work

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

Year: 2025

Type: article

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.

Source: Communications in Analysis and Mechanics

DOI: 10.3934/cam.2025026

Authors: Marvin Koonce, Jason Metcalfe

Institution: University of North Carolina at Chapel Hill

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: RTG: Partial Differential Equations on Manifolds, Dispersive and Wave Equations in the Presence of Background Geometry