navier-stokes

[verdigris]

Why is there a prize of $1 million for showing that there are smooth solutions to the Navier-Stokes equations throughout time.Why isn't the prize being offered for finding what the solutions actually are?

[arildno]

There are an infinity of solutions to N-S, many of which are well-known.

Infinity*$1million=more money that we'll ever get.

Besides, it is more important to understand the fundamental structure of all solutions, rather than the details of any particular solution.

To demonstrate that, for smooth boundary conditions&initial values, no solution will blow up in finite time, would deepen our understanding of the fundamental structure of N-S solutions.

[verdigris]

How would knowing the fundamental structure of all solutions be of practical use in,say,aerodynamics?

[arildno]

If you don't attach any sort of value to mathematical insights in themselves, you might as well remain a caveman.

I refuse to answer that question.

[arildno]

Another thing:
Finding approximate solutions to the accuracy needed for practical purposes, are generated every day by professionals already.
So, in this sense, to find solutions isn't "challenging" in the sense that professionals know how to get them.