Microlocal Partition of Energy for Fractional-Type Dispersive Equations
Analysis of PDEs
2025-09-10 v1
Abstract
This paper is devoted to the proof of microlocal partition of energy for fractional-type dispersive equations including Schr\"odinger equation, linearized gravity or capillary water-wave equation and half-Klein-Gordon equation. Roughly speaking, a quarter of the energy lies inside or outside the "light cone" 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.
Keywords
Cite
@article{arxiv.2309.15282,
title = {Microlocal Partition of Energy for Fractional-Type Dispersive Equations},
author = {Haocheng Yang},
journal= {arXiv preprint arXiv:2309.15282},
year = {2025}
}