此問題與著名的千禧年大獎數學問題(Millennium Prize Problems)密切相關。 2000年5月24日，美國的 Clay Mathematical Institute 發布了7個千禧年大獎問題。其中之一是關於Navier-Stokes方程。Clay Institute 在其網頁上用簡短生動的語言介紹了這一問題
‘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.’
參考文獻 [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)
