 the RH, the 3DNSE and the YME millennium problemsDisclaimer: all papers of the sections AC are without authorization from the ivory tower for latest updates and related papers see www.riemannhypothesis.de www.unifiedfieldtheory.de www.eulermascheroniconstant.de A. A new integral and series representation of Riemann's symmetrical functional equation to prove the Riemann Hypothesis
B. A global unique H(1/2) (potential energy) inner product based weak solution of the 3DNavierStokes equations We provide a global unique (weak, generalized Hopf) H(1/2)solution of the generalized 3D NavierStokes 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 nonlinear term (1959). The extended (energy) Hilbert space is in line with the proposed quantum potential energy space as proposed in section C. It provides a mathematical model for Mie's theory accompanied by Mie’s concept of an electric pressure enhancing the Maxwell equations. Mie's concept can be applied to the second unknown function in the NSE, 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 CalderónZygmund integrodifferential operator applied to the (velocity) NSEsolution 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 C. A Krein space based quanta energy field theory www.unifiedfieldtheory.de
Abstract
A Krein space based matter field theory is provided. From the Mie theory the concept of discrete energy knots is taken modelled by a physical problem specific (selfadjoint) kinetic energy operator. From the correspondingly defined Krein space framework the concept of a (selfadjoint) potential energy operator is applied. It enables the definition of potential energy norms on all of the Krein space built on sets of quantum numbers leading to a (vacuum, plasma, MaxwellNewtonMie) grouping of mechanical and dynamical quantum energy element types. The proposed model provides an appropriate framework for the Mie theory, which is an enhanced Maxwell theory accompanied by the concept of an electric pressure. This Mie theory makes the YME and its underlying mass gap problem obsolete.
D. PhD thesis
The paper includes a proof of the quasioptimal approximation behavior of the RitzGalerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (PseudoDifferential) integral operator. Other examples would be the CalderonZygmund (singular integral) operator or the Hilbert transform (singular integral) operator.
