论文标题
三维不可压缩的Euler方程
Leapfrogging vortex rings for the 3-dimensional incompressible Euler equations
论文作者
论文摘要
流体动力学中的一个经典问题涉及多个涡流环的相互作用，该环在不可压缩的，无粘性的$ 3 $维液中共享对称性的共同轴。 Helmholtz（1858）观察到，由于彼此作用的环的诱导流动的流动，一对类似的薄薄，同轴涡流环可能会反复穿过。这种著名的配置被称为Leapfrogging，尚未得到严格建立。我们通过构造表现出这种运动模式的3D Euler方程的平滑解决方案来为该现象提供数学上的理由。
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid $3$-dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3d Euler equations exhibiting this motion pattern.
