标题： 辛表示和不可压缩Navier-Stokes方程的湍流全局解在$\R^3$ 显示英文标题

标题： Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$

摘要： 不可压缩的纳维-斯托克斯方程被考虑。 我们发现存在无限多个非平凡的静态欧拉方程解。 此外还存在静态欧拉方程的随机解。 当雷诺数足够大且时间变量$t$趋于无穷时，这些静态欧拉方程的随机解是相应纳维-斯托克斯流的路径极限。 但这些纳维-斯托克斯流的双重极限不存在。 因此这些解被称为湍流解。 显示英文摘要

摘要： The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large enough and time variable $t$ goes to infinity, these random solutions of static Euler equations are the path limits of corresponding Navier-Stokes flows. But the double limit of these Navier-Stokes flows do not exist. Therefore these solutions are called turbulent solutions.