二维Euler稳态流与三维轴对称光滑Euler流的增长

Two-Dimensional Stationary Euler Flows and the Growth of Three-Dimensional Axisymmetric Smooth Euler Flows

研究三维轴对称Euler方程组光滑解的增长,目的是对三维Euler方程组找尽可能快增长的解,探索方程组的全局正则性。通过适当选取速度场的一个分量,可把三维轴对称Euler方程组去耦,从而给出一族三维光滑无界轴对称区域及其上Euler方程组对时间有指数增长的轴对称全局光滑解。通过类似的方法得到多种平面区域上Euler方程的显式稳态解。

A study was made of the growth of smooth three-dimensional axisymmetric incompressible Euler flows.The goal was to find flows of fastest possible growth and investigate the global regularity issue of the three-dimensional Euler equations.Through aptly choosing a velocity component,the three-dimensional axisymmetric Euler system can be decoupled with a family of three-dimensional smooth unbounded axisymmetric domains and smooth solutions of the Euler equations with exponential growth on them constructed.Similar methods were used to obtain stationary Euler flows in various planar domains.