Navier-Stokes Equations, the millenium problem solution

This homepage was built 2016 to present the paper

Global Existence and Uniqueness
of the Non-stationary 3D-Navier-Stokes
Initial-boundary Value Problem
Dr. Klaus Braun
June, 2016

The paper itself is not outdated, however there is a new homepage, which explains the H(1/2) energy space as a Hilbert space based approximation model of the underlying Krein space based new unified quanta field model.

https://www.fuchs-braun.com/

Background

The central conceptual concept of the paper above is a new kind of energy:
The current mechanical energy type provides kinetical and potential energy. The prize to be paid for this only mechanical physical view on Nature are two mathematically different force types, the volume forces (associated with mass densitities, average volocities/accelerations of fluids) and the surface force (associated with friction, viscocity, pressure etc.). The related model problem is called the d’Alembert paradox. It turned out that the standard mechanical energy Hilbert space based on the self-adjoint Friedrichs extension of the symmetric Laplacian operator, the Hilbert space H(1), extended by its complementary sub-space in an overall H(1/2) energy Hilbert space provides an appropriate model for a new dynamic type.

The new concept was not accepted for understandable reasons at that point in time. As a consequence during the last decade the author developed a new quantum field theory, which explains the H(1/2) energy space as a Hilbert space based approximation model of the underlying Krein space based new unified quanta field model.

"In fact, to date, 3D regular flows are known to exist either for all times but for data of "small size", or for data of "arbitrary size" but for a finite interval of time only, .... it is not known whether, in the 3D case, the associated initial-boundary value problem is well-posed in the sense of Hadamard, ...

"The prescription of the pressure p as a solution of the Neumann problem at the boundary walls or at the initial time is independently of the velocity v and, therefore, could be incompatible with the initial-boundary value NSE problem, which could render the problem ill-posed."

G. P. Galdi, The NSE: A Mathematical Analysis