### Tuesday, 12 October 2004 - 4:45 PM

### This presentation is part of : Rajagopal Symposium

### Some Issues Related to the N--S Equations

**L Tao**, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123 and G Q Chen, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China.
We discuss three issues related to the Navier-Stokes (N-S) equations. (i) From the experimental data of Perry's on Brownian motion we may infer that a determinate description on the motion of water at the spatial scales below than 0.1mm may be inadequate. A possible implication of this bound on the N-S equations will be discussed. (ii) For a discrete model constructed according to the N-S equations in the macroscopic limit, the bound mentioned above gives some indication in general about the size of the cells appropriate for simulating the motion of water. Moreover, theory of stochastic differential equations may provide us a framework to construct discrete models. (iii) A possible large eddy simulation model, on the basis of the N-S equations and the assumption of similarity, will be discussed.

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