On the Fourth order Schr\'odinger equation in three dimensions: dispersive estimates and zero energy resonances
| Autor: | Erdogan, Burak, Green, William R., Toprak, Ebru |
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| Rok vydání: | 2019 |
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| Zdroj: | J. Differential Equations, 271, (2021), 152-185 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2020.08.019 |
| Popis: | We study the fourth order Schr\"odinger operator $H=(-\Delta)^2+V$ for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and study the dynamic effect of each on the $L^1\to L^\infty$ dispersive bounds. In all cases, we show that the natural $|t|^{-\frac34}$ decay rate may be attained, though for some resonances this requires subtracting off a finite rank term, which we construct and analyze. The classification of these resonances, as well as their dynamical consequences differ from the Schr\"odinger operator $-\Delta+V$. Comment: 35 pages, submitted. arXiv admin note: text overlap with arXiv:1810.03678 |
| Databáze: | arXiv |
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