论文标题
相对论弗拉索夫方程的大数据和半经典限制的矩传播
Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
论文作者
论文摘要
我们调查了半经典的限制，从半偏见的hartree-fock方程式描述了均值分散定律中均衡状态中的fermions系统的时间演变，并通过$ k（x）=γ\ frac {1}} {1}} {| x | x | x $ a} $ k（x）= frac（x）= frac（x）的奇异潜力进行交互（ \ frac {d} {2} -2， - 1 \ right \}，d -2 \ right] $，$ d \ in \ {2,3 \} $和$γ\ in \ in \ mathbb {r} $，带有约定的$ k（x）=γ\ log（| x | x |）$ a = 0 $，向相对论的vlasov方程式转变为具有奇异电位的vlasov方程，从而概括了172（2），398--433（2018）。
We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relativistic dispersion law and interacting through a singular potential of the form $K(x)=γ\frac{1}{|x|^a}$, $a \in \left( \max \left\{ \frac{d}{2} -2 , - 1 \right\}, d-2 \right]$, $d\in\{2,3\}$ and $γ\in\mathbb{R}$, with the convention $K(x)=γ\log(|x|)$ if $a=0$. For mixed states, we show convergence in Schatten norms with explicit rate towards the Weyl transform of a solution to the relativistic Vlasov equation with singular potentials, thus generalizing [J. Stat. Phys. 172 (2), 398--433 (2018)] where the case of smooth potentials has been treated. Moreover, we provide new results on the well-posedness theory of the relativistic Vlasov equations with singular interactions.
