论文标题
二维Euler方程的点涡流爆发和非唯一性
Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations
论文作者
论文摘要
我们为Euler Point涡流系统提供了严格的解决方案的结构，其中三个涡流在许多涡流的配置中爆发出一个涡流，或者等效地存在任意的许多涡流的配置，其中三个涡流中的三个在有限的时间内崩溃了。作为中间步骤，我们表明，在足够规则的外部扰动下，平面中三个孤立涡流的众所周知的自相似爆发和崩溃。我们还讨论了我们的结果如何为二维Euler方程（从Schochet引入的意义上）产生非唯一弱解的示例，其中能量被消散。
We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist configurations of arbitrarily many vortices in which three of them collapse in finite time. As an intermediate step, we show that well-known self-similar bursts and collapses of three isolated vortices in the plane persist under a sufficiently regular external perturbation. We also discuss how our results produce examples of non-unique weak solutions to 2-dimensional Euler's equations -- in the sense introduced by Schochet -- in which energy is dissipated.
