A global unique H(1/2) (potential energy) inner product based weak solution of the 3D-Navier-Stokes equations

We provide a global unique (weak, generalized Hopf) H(1/2)-solution of the generalized 3D Navier-Stokes initial value problem. The global boundedness of a generalized energy inequality with respect to the energy Hilbert space H(1/2) is a consequence of the Sobolevskii estimate of the non-linear term (1959). The extended (energy) Hilbert space is in line with the proposed Krein space based quanta potential energy Hilbert space concept in unified-field-theory.de. It enables an alternative mathematical model for Mie’s concept of an electric pressure enhancing the Maxwell equations. The second unknown function in the NSE is the pressure p;  the pressure function p can be represented as Riesz operator transforms of (u x u), while the gradient (force) operator applied to the unknown pressure function p becomes the Calderón-Zygmund integrodifferential operator applied to the (velocity) NSE-solution function u (EsG) p. 44.

For more details concerning the H(1/2) "potential energy" inner product we refer to the following section C. Further supporting papers are