论文标题
具有奇异相互作用力的动力学vlasov-fokker-planck方程的量化过度阻尼极限
Quantified overdamped limit for kinetic Vlasov-Fokker-Planck equations with singular interaction forces
论文作者
论文摘要
我们建立了具有非局部相互作用力的动力学vlasov-fokker-Planck方程的定量压缩极限。我们在该动力学方程和限制方程之间的解决方案之间的误差方面提供了明确的界限，该方程以聚合 - 扩散方程或McKean-Vlasov方程的名称而闻名。通过粗粒度图引入中间系统，我们定量估计vlasov-fokker-planck方程的空间密度之间的误差与订单的订单距离中的中间系统之间的误差2。然后，我们得出了一个流动的梯度流动，使我们之间的流动范围的流动范围是误差，从而使我们之间的误差量相互量化。我们的策略仅需要相互作用势的弱集成性，因此特别是它包括具有排斥性静电或有吸引力的重力相互作用的动力学Vlasov-Poisson-Fokker-Planck系统的量化过度阻尼的极限。
We establish a quantitfied overdamped limit for kinetic Vlasov-Fokker-Planck equations with nonlocal interaction forces. We provide explicit bounds on the error between solutions of that kinetic equation and the limiting equation, which is known under the names of aggregation-diffusion equation or McKean-Vlasov equation. Introducing an intermediate system via a coarse-graining map, we quantitatively estimate the error between the spatial densities of the Vlasov-Fokker-Planck equation and the intermediate system in the Wasserstein distance of order 2. We then derive an evolution-variational-like inequality for Wasserstein gradient flows which allows us to quantify the error between the intermediate system and the corresponding limiting equation. Our strategy only requires weak integrability of the interaction potentials, thus in particular it includes the quantified overdamped limit of the kinetic Vlasov-Poisson-Fokker-Planck system to the aggregation-diffusion equation with either repulsive electrostatic or attractive gravitational interactions.
