Global-in-time Semiclassical Regularity for the Hartree-Fock Equation
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916087458693120 |
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| author | Chong, Jacky J. Lafleche, Laurent Saffirio, Chiara |
| author_facet | Chong, Jacky J. Lafleche, Laurent Saffirio, Chiara |
| contents | For arbitrarily large times $T>0$, we prove the uniform-in-$\hbar$ propagation of semiclassical regularity for the solutions to the Hartree$\unicode{x2013}$Fock equation with singular interactions of the form $V(x)=\pm\,|x|^{-a}$ where $a\in(0,\frac12)$. As a byproduct of this result, we extend to arbitrarily long times the derivation of the Hartree$\unicode{x2013}$Fock and the Vlasov equations from the many-body dynamics provided in [J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_13998 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global-in-time Semiclassical Regularity for the Hartree-Fock Equation Chong, Jacky J. Lafleche, Laurent Saffirio, Chiara Analysis of PDEs Mathematical Physics 35Q55, 35B65, 82C10, 81Q20 For arbitrarily large times $T>0$, we prove the uniform-in-$\hbar$ propagation of semiclassical regularity for the solutions to the Hartree$\unicode{x2013}$Fock equation with singular interactions of the form $V(x)=\pm\,|x|^{-a}$ where $a\in(0,\frac12)$. As a byproduct of this result, we extend to arbitrarily long times the derivation of the Hartree$\unicode{x2013}$Fock and the Vlasov equations from the many-body dynamics provided in [J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)]. |
| title | Global-in-time Semiclassical Regularity for the Hartree-Fock Equation |
| topic | Analysis of PDEs Mathematical Physics 35Q55, 35B65, 82C10, 81Q20 |
| url | https://arxiv.org/abs/2202.13998 |