论文标题
在粘性2D流中的涡流动力学上
On the dynamics of vortices in viscous 2D flows
论文作者
论文摘要
我们研究了2D Navier - 史托克斯解决方案，从初始涡度开始，该涡度温和浓度接近$ n $ n $不同的点。我们证明了关于Helmholtz和Kirchhoff引入的相互作用点涡流系统附近浓度的传播的定量估计。我们的工作以三种方式扩展了文献中先前的结果：最初的涡度集中在弱（Wasserstein）意义上，它仅是$ l^p $对于某些$ p> 2 $的集成，而我们得出的估计在粘度方面是统一的。
We study the 2D Navier--Stokes solution starting from an initial vorticity mildly concentrated near $N$ distinct points in the plane. We prove quantitative estimates on the propagation of concentration near a system of interacting point vortices introduced by Helmholtz and Kirchhoff. Our work extends the previous results in the literature in three ways: The initial vorticity is concentrated in a weak (Wasserstein) sense, it is merely $L^p$ integrable for some $p>2$, and the estimates we derive are uniform with respect to the viscosity.
