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Pré-Publication, Document De Travail Année : 2023

Microlocal Partition of Energy for Fractional-Type Dispersive Equations

Résumé

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 $L^2$ 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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Dates et versions

hal-04219225 , version 1 (26-09-2023)

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  • HAL Id : hal-04219225 , version 1

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Haocheng Yang. Microlocal Partition of Energy for Fractional-Type Dispersive Equations. 2023. ⟨hal-04219225⟩
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