Microlocal Partition of Energy for Fractional-Type Dispersive Equations

2023/09/26 by Haocheng Yang, Yang, Haocheng
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2309.15282

openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the proof of microlocal partition of energy for fractional-type dispersive equations including Schrödinger equation, linearized gravity or capillary water-wave equation and half-Klein-Gordon equation. Roughly speaking, a quarter of the L² energy lies inside or outside the "light cone" |x| = |tP'(ξ)| for large time. In addition, based on the study of half-Klein-Gordon equation, the microlocal partition of energy will also be proved for Klein-Gordon equation.

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