论文标题
具有乘法噪声的随机点涡流系统的平均场极限
The Mean-Field Limit of Stochastic Point Vortex Systems with Multiplicative Noise
论文作者
论文摘要
在ARXIV中：1004.1407，Flandoli，Gubinelli和Priola提出了Helmholtz和Kirchoff经典点涡流系统的随机变体，其中将传输类型的乘法噪声添加到动力学中。此后几年的一个开放问题是表明，在平均场缩放方案中，循环与涡旋数量成反比，系统的经验度量会收敛到具有多种噪声的二维Euler涡流方程的解决方案。通过开发用于确定性粒子系统的平均场限制的调制能量和Duerinckx的调制能量方法，以及通过作者引入的思想来构建用于在平均场方程的缩放量规则性上研究此类限制的想法，我们在最小的假设下求解了这个问题。
In arXiv:1004.1407, Flandoli, Gubinelli, and Priola proposed a stochastic variant of the classical point vortex system of Helmholtz and Kirchoff in which multiplicative noise of transport-type is added to the dynamics. An open problem in the years since is to show that in the mean-field scaling regime, in which the circulations are inversely proportional to the number of vortices, the empirical measure of the system converges to a solution of a two-dimensional Euler vorticity equation with multiplicative noise. By developing a stochastic extension of the modulated-energy method of Serfaty and Duerinckx for mean-field limits of deterministic particle systems and by building on ideas introduced by the author for studying such limits at the scaling-critical regularity of the mean-field equation, we solve this problem under minimal assumptions.
