Microlocal Partition of Energy for Fractional-Type Dispersive Equations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908525783941120 |
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| author | Yang, Haocheng |
| author_facet | Yang, Haocheng |
| contents | 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" $|x| = |tP'(ξ)|$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Microlocal Partition of Energy for Fractional-Type Dispersive Equations Yang, Haocheng Analysis of PDEs 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" $|x| = |tP'(ξ)|$ 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. |
| title | Microlocal Partition of Energy for Fractional-Type Dispersive Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2309.15282 |