Analytic Solution of Navier-Stokes

Analytic Solution of the N-Dimensional Incompressible Navier-Stokes Equations

The paper linked above presents an analytic solution to the Navier-Stokes equations that I believe solves the Clay Math Institute’s Millennium problem on the existence and smoothness of the Navier-Stokes equations.

I have submitted this paper to a journal and I am waiting to hear back. I am sharing a pre-print on my website because I am very excited about the result.

What is an “Analytic Solution”?

By “analytic solution”, I mean a solution in terms of analytic functions. I.e., in terms of functions that can be expressed as convergent Taylor series. Such solutions can be “closed form solutions” consisting of arithmetic operations (addition, subtraction, multiplication, division, or integer powers) on other analytic functions and constants. However, they can also be expressed as “recurrence relations” that are formulae for the coefficients of the Taylor series expansion of an analytic function in terms of other known quantities. This analytic solution is the latter kind.

Is this correct?

I don’t know if this is correct, but I have tried my best to find any errors or mistakes. I am sharing it here so that my friends, colleagues, or others who stumble upon this link can take a look and see if they can find any problems. If you find something wrong, I would appreciate if you sent me a note to (my first name)(at)visviva.space.

How long have I been working on this?

I have been working on series algebra methods for solving differential equations for about 25 years. I have mostly concentrated on problems useful in astrodynamics, but these methods can be applied to any system of partial or ordinary differential equations. Since setting out on my own with Vis Viva, I have been developing formal proofs to support these methods. This paper is just my first result with these new techniques, and I hope to have a paper out on the full set of techniques soon.