Towards a mathematical theory of fluid turbulence via singular vortex dynamics

指出流体动力学方程的耗散弱解对理解湍流统计理论具有重要作用。但这种奇异解的存在性尚未得到证明，其动力学性质也是不确定的。在本课题中，我们成功地得到了α点涡系的自相似塌缩解。这是二维欧拉方程的耗散弱解，它具有二维湍流中观察到的重要性质之一。

It has been pointed out that dissipative weak solutions of the hydrodynamic equations plays an important role in understand the statistical theory of turbulence. But the existence of such a singular solution has not yet proven and its dynamical property is uncertain. In the present project, we successfully obtain a self-similar collapsing solution of α point vortex system. This is a dissipative weak solution of 2D Euler equation, which acquires one of the important properties observed in 2D turbulence.