论文标题
Hartree-fock方程式的全球半经典规律性
Global-in-time Semiclassical Regularity for the Hartree-Fock Equation
论文作者
论文摘要
对于任意的时间$ t> 0 $，我们证明了统一 - $ \ hbar $在半经典规律性的繁殖方面，用于hartree $ \ unicode {x2013} $ fock方程，并具有$ v（x）= \ pm \ pm \，| x | x | x | x | a}的单数相互作用，$ v（x）作为此结果的副产品，我们将hartree $ \ unicode {x2013} $ fock和vlasov方程的派生延伸到任意长时间。 Chong，L。Lafleche，C。Saffirio：Arxiv：2103.10946（2021）]。
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)].
