The Lorenz equation as a metaphor for the Navier-Stokes equations
The Lorenz equation as a metaphor for the Navier-Stokes equations
复制标题
洛伦兹方程作为纳维-斯托克斯方程的隐喻
DOI：
10.3934/dcds.2001.7.403
复制
发表时间：
2001
影响因子：
1.1
通讯作者：
E. Titi
中科院分区：
文献类型：
--
作者：
C. Foias;M. Jolly;I. Kukavica;E. Titi
严格研究2D的三种方法
Navier-Stokes方程（NSE）被应用到Lorenz系统。
对时间平均解的分析导致对
Lorenz吸引子上的不变概率测度，
比已知的NSE要完整得多。就是这种情况
对于NSE，Lorenz吸引子的解是解析的，
绕着真实的时间轴旋转严格的估计是结合
用泰勒系数的数值计算来估计
这条带的宽度。最初的近似惯性形式
为NSE开发的Lorenz系统进行了分析，
对后者的动力学进行了完整的描述。
Three approaches for the rigorous study of the 2D
Navier-Stokes equations (NSE) are applied to the Lorenz system.
Analysis of time averaged solutions leads to a description of
invariant probability measures on the Lorenz attractor which is
much more complete than what is known for the NSE. As is the case
for the NSE, solutions on the Lorenz attractor are analytic in a
strip about the real time axis. Rigorous estimates are combined
with numerical computation of Taylor coefficients to estimate the
width of this strip. Approximate inertial forms originally
developed for the NSE are analyzed for the Lorenz system, and the
dynamics for the latter are completely described.