måndag 25 april 2016

Reformulation of Clay Navier-Stokes Problem Needed 2

The official formulation of the Clay Navier-Stokes Problem is unfortunate by not mentioning the Reynolds number $Re =\frac{UL}{\nu}$ with $U$ a typical flow speed, $L$ length scale, and $\nu$ viscosity scale, and thereby making no distinction between laminar/smooth flow at small Reynolds numbers and turbulent/non-smooth flow at large Reynolds numbers.

Instead the problem is formulated so as lead people to seek a solution in the form of blow-up (or not blow-up) to infinity of flow speeds in finite time, following a simple methodology borrowed from ordinary differential equations saying that as long as a solution trajectory is finite it can be continued for some time. But this is not the real issue for a partial differential equation like Navier-Stokes, where the essential distinction is instead between laminar/smooth and turbulent/non-turbulent flow.

The result is a problem formulation which is meaningless because it is both unphysical and unmathematical, and as such cannot be given a meaningful answer.

The problem is owned by a small group of pure mathematicians including Fefferman and Tao, who refuse to participate in any form of discussion about the problem and its formulation. This is not in the interest of anybody outside this group and thus not in the general interest of mathematics as science, which must be the interest of mr Clay in particular...


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