三维不可压Euler方程的动力学

Dynamics of the 3D Incompressible Euler Equation

考虑三维不可压Euler方程的一些物理量沿质点轨迹的演化情况。Chae已考虑了涡量沿质点轨迹增加的情景,文章考虑令解衰减、系统稳定的另一种情景,进而把系统的演化情况(包括它在两种情景间的转化、爆破或衰减)作完整的描述。推广了Chae已考虑的情景的结果,得到更强的结论。

A study is made of the evolutions along particle trajectories of some physical quantities of the three dimensional incompressible Euler equation. In the literature, Chae has considered the scenario in which the magnitude of the vorticity increases along particle trajectories. In this article, a discussion is made of another scenario which results in decaying solutions and stable systems. Consequent- ly, a complete description of the evolution of the Euler system can be given, including the changing of scenarios, blowing up and decay of the solution. Chae＇ s results in the scenario he has considered are al- so generalized.