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Vortex dynamics for 2D Euler flows with unbounded vorticity
Revista Matemática Iberoamericana ( IF 1.2 ) Pub Date : 2021-02-01 , DOI: 10.4171/rmi/1255
Stefano Ceci 1 , Christian Seis 1
Affiliation  

It is well known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff–Routh point vortex system. In this paper, we revisit the classical problem of how well solutions to the Euler equations approximate these vortex dynamics, and extend previous rigorous results to the case where the vorticity field is unbounded. More precisely, we establish estimates for the 2-Wasserstein distance between the vorticity and the empirical measure associated with the point vortex dynamics. In particular, we derive an estimate on the order of weak convergence of the Euler solutions to the solutions of the point vortex system.

中文翻译:

具有无界涡度的二维欧拉流的涡流动力学

众所周知,理想的不可压缩二维流体中的涡流动力学是由 Kirchhoff-Routh 点涡系统描述的。在本文中,我们重新审视了欧拉方程的解如何很好地近似这些涡流动力学的经典问题,并将先前的严格结果扩展到涡量场无界的情况。更准确地说,我们建立了涡度和与点涡流动力学相关的经验测量之间的 2-Wasserstein 距离的估计值。特别是,我们推导出了欧拉解对点涡系统解的弱收敛阶数的估计。
更新日期:2021-02-01
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