Mean field limit for Coulomb-type flows
Mean field limit for Coulomb-type flows
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DOI：
10.1215/00127094-2020-0019
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发表时间：
2018-03
影响因子：
2.5
通讯作者：
S. Serfaty;appendix with Mitia Duerinckx
中科院分区：
文献类型：
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作者：
S. Serfaty;appendix with Mitia Duerinckx
当相互作用是库仑势或超库仑Riesz势时，我们首次在任意维中建立了点系沿相互作用能梯度流沿着演化的平均场收敛性.证明是基于调制能量方法，使用库仑或Riesz距离，假设的极限方程的解决方案是足够的规则，并利用弱-强稳定性属性。该方法可以处理增加一个定期的相互作用的核心，也适用于保守和混合流。在附录中，它也适用于证明平均场收敛的解决方案，牛顿定律与库仑或Riesz相互作用的单动力学的情况下的解决方案的欧拉-泊松型系统。
We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary dimension. The proof is based on a modulated energy method using a Coulomb or Riesz distance, assumes that the solutions of the limiting equation are regular enough and exploits a weak-strong stability property for them. The method can handle the addition of a regular interaction kernel, and applies also to conservative and mixed flows. In the appendix, it is also adapted to prove the mean-field convergence of the solutions to Newton's law with Coulomb or Riesz interaction in the monokinetic case to solutions of an Euler-Poisson type system.