an:07269204
Zbl 1451.35120
Cao, Daomin; Wan, Jie; Zhan, Weicheng
Desingularization of vortex rings in 3 dimensional Euler flows
EN
J. Differ. Equations 270, 1258-1297 (2021).
00454788
2021
j
35Q31 76B47 35B40
incompressible Euler system; vortex rings; inviscid limit
Summary: In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a jump in vorticity at the boundary of the cross-section of the vortex ring. Using the vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in several kinds of domains. The precise localization of the asymptotic singular vortex filament is proved to depend on the circulation and the velocity at far fields of the vortex ring, and the geometry of the domains. Some qualitative and asymptotic properties are also established.