论文标题
全球制服$ n $估计用于hartree-fock-bogoliubov类型的解决方案的估算值
Global uniform in $N$ estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime
论文作者
论文摘要
我们将Chong等人（2022）的最新工作扩展到关键案例。更准确地说，我们证明了全球时间，在$ n $估计的$ n $估计值$ ϕ $，$λ$和$γ$的$ n $估计值中，hartree-fock-bogoliubov类型的耦合系统具有相互作用的潜在$ \ frac1nv_n（x-y）（x-y）（x-y）= n^{2} v（n^{2} v（x y（x-y））$。我们假设潜在的$ V $很小，可以满足某些技术条件，并且初始条件具有有限的能量。主要成分是对线性schrödinger方程的尖锐估计值，其潜力在6+1维度中，这本身可能引起人们的关注。
We extend the recent work of Chong et al., (2022) to the critical case. More precisely, we prove global in time, uniform in $N$ estimates for the solutions $ϕ$, $Λ$ and $Γ$ of a coupled system of Hartree--Fock--Bogoliubov type with interaction potential $\frac1NV_N(x-y)=N^{2}v(N(x-y))$. We assume that the potential $v$ is small which satisfies some technical conditions, and the initial conditions have finite energy. The main ingredient is a sharp estimate for the linear Schrödinger equation with potential in 6+1 dimension, which may be of interest in its own right.
