论文标题
Vlasov-Poisson-Fokker-Planck模型的扩散极限：定量和强收敛结果
Diffusive limit of the Vlasov-Poisson-Fokker-Planck model: quantitative and strong convergence results
论文作者
论文摘要
这项工作解决了Vlasov-Poisson-Fokker-Planck模型的扩散极限。我们得出先验估计值，该估计不限制相位空间维度，并提出强大的收敛导致L2空间。此外，如果初始数据在某些足够大的LP空间中，我们通过任意接近（正式）最佳速率的明确收敛速率来加强先前的结果。我们的结果存在于有界的时间间隔，其大小在渐近极限中以显式下限在渐近极限中生长到无穷大。该分析依赖于确定正确的相空间坐标集来研究感兴趣的制度。在这组坐标中，有限模型明确出现。
This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck model. We derive a priori estimates which hold without restriction on the phase-space dimension and propose a strong convergence result in a L2 space. Furthermore, we strengthen previous results by obtaining an explicit convergence rate arbitrarily close to the (formal) optimal rate, provided that the initial data lies in some Lp space with p large enough. Our result holds on bounded time intervals whose size grow to infinity in the asymptotic limit with explicit lower bound. The analysis relies on identifying the right set of phase-space coordinates to study the regime of interest. In this set of coordinates the limiting model arises explicitly.
