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arXiv · 2309.15282

Microlocal Partition of Energy for Fractional-Type Dispersive Equations

Haocheng Yang
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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 $L^2$ energy lies inside or outside the "light cone" $|x| = |tP'(\xi)|$ 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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Haocheng Yang. 2023-09-26. Microlocal Partition of Energy for Fractional-Type Dispersive Equations. https://doi.org/10.2140/apde.2025.18.2081

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