此问题与著名的千禧年大奖数学问题(Millennium Prize Problems)密切相关。 2000年5月24日，美国的 Clay Mathematical Institute 发布了7个千禧年大奖问题。其中之一是关于Navier-Stokes方程。Clay Institute 在其网页上用简短生动的语言介绍了这一问题
‘Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.’
参考文献 [1] T.H.Solomon and J.P. Gollub, Chaotic particle transport in time-dependent Rayleigh-Benard convection , Physical Review A. Vol.38 No. 12, (1988) 6280-6286 [2] S. Wiggins, The dynamical systems approach to Lagrangian transport in oceanic flows, Annu. Rev. Fluid Mech. 37, (2005) 295–328. [3] N. Malhotra and S. Wiggins, Geometric Structures, Lobe Dynamics, and Lagrangian Transport in Flows with Aperiodic Time-Dependence, with Applications to Rossby Wave Flow,J. Nonlinear Sci. Vol. 8: pp. 401–456 (1998)
