måndag 19 maj 2014

Wellposedness and Turbulence Not Part of Clay Navier-Stokes Problem!

A central aspect of the mathematical theory of partial differential equations, such as the incompressible Navier-Stokes equations, concerns wellposedness, which is the sensitivity of solutions with respect to perturbations of data in suitable quantitative form. Without wellposedness in some form solutions have no permanence and meaning, since they can change arbitrarily subject to virtually nothing.

But the Official Description of Clay Navier-Stokes Prize Problem does not include the aspect of wellposedness.

A central aspect of incompressible flow described by the Navier-Stokes equations, is turbulence. 

But the Official Description of the Clay Navier-Stokes Prize Problem does not include any aspect of turbulence.

The Official Description is thus questionable, to say the least, from both mathematical and physical point of view, by leaving out what is fundamental.

When I point this out to Charles Fefferman who has formulated the Official Description of the problem, and Luis Cafarelli who gives a video presentation thereof, and Peter Constantin who acts as referee to evaluate proposed solutions and Terence Tao who works to solve the problem and to the President of the Clay Institute, I get no reaction but silence.

This is not reasonable, since the Navier-Stokes equations and the mathematics thereof belongs to us all and thus must be open to public discussion, in particular so when it has been elevated to a Millennium Prize Problem of importance to humanity.

I sent to following renewed request to the people involved to reveal their cards:

Dear Colleagues:

I try to get a response from you concerning my questioning of the Official Description of Clay Navier-Stokes Prize Problem expressed here

I get no response but compact silence. I don't think this is in the interest of a Clay Prize Problem as of concern to a wide mathematical and scientific community and not secluded to a very small closed circle.

The omission of both wellposedness and turbulence in the Official Description lacks rationality from both mathematical and physical point of view, and irrationality is against the principles of mathematics and physics.

I hope you can see that my questioning requires a response from you in your respective roles.

Sincerely, Claes Johnson

PS I raised the same question a couple of  years ago, and the only response then on my question how the Prize problem could be meaningful without including the aspect of wellposednes , was Fefferman's short reply: "It is meaningful to me". I think this answer misses that fact that science is not only a private thing.

Inga kommentarer:

Skicka en kommentar