Developments of the mathematical research of the system of 2D point vortices

该研究项目的目的是考虑和发展点涡系统作为二维涡运动模型的数学方面。作为该模型的特点之一，我们研究了涡旋坍缩问题，并将二维自相似坍缩解推广到三维的自相似坍缩解。我们还研究了作为二维和三维湍流中间的稳定分层湍流的统计特性，并研究了它们在维数上的差异。

The objective of the research project was to consider and develop the mathematical aspects of the point vortex system as a model for two dimensional vortex motions. As one of the characteristics of the model, we have studied the problem of vortex collapse, and extended the 2D self-similar collapse solution into one in three dimensions. We have also studied the statistical properties of stably stratified turbulence as a middle of 2D and 3D turbulence, and investigated the difference in the dimensionality.