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MAIN OPEN PROBLEMS

It is however entirely possible that singular solutions exist but are unstable and therefore difficult to construct analytically and impossible to detect numerically.

CONJECTURE

3 Global Regularity for Navier-Stokes

_t u+u __ u- __u = -_p

div u= 0

NOTE OF CAUTION

Break-down requires infinite velocities--unphysical:


• incompatible with relativity
• thin regions of infinite velocities are incompatible with the assumption of small mean free path required in the macroscopic derivation of the equations.

The solutions corresponding to generic, regular initial data can be continued for all tç0.

The solutions corresponding to all regular initial data can be smoothly continued for all tç0.

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