What is the physical application of Navier-Stokes existence and smoothness?

Recently, mathematician Mukhtarbay Otelbaev published a paper Existence of a strong solution of the Navier-Stokes equations, in which he claim that he solved one of the Millennium Problems: Existence and smoothness of the Navier-Stokes equation.

What is physical application of the problem that Prof. Otelbaev proved about turbulence?

• Do you really mean "physical application", or more "practical application"? – Bernhard Jun 24 '14 at 5:51
• See this Q/A on the Math SE and the links within it e.g. to Terry Tao's paper. The maths is waaaay beyond me, but it looks as if Prof Otelbaev has at best proved only a solution for a special case. – John Rennie Jun 24 '14 at 6:14

1 Answer

IANAFD but I'll stick my neck out and say this: resolving the Clay problem one way or another won't cause people doing CFD to lose any more sleep than they already do.

First of all, Jean Leray proved the existence of weak solutions to Navier Stokes in $R^3$ way back in the 1930s, and that is pretty much what matters for the task of getting numerical solutions. (Their uniqueness is a different story.)

Secondly, there is an even stronger result from Caffarelli, Kohn and Nirenberg (1982) which makes it clear that a singularity, if it exists, cannot fill a line in spacetime. It must be ephemeral, and is therefore unlikely to have anything to do with turbulence.