Disclaimer: this homepage is no longer maintained; nevertheless, it contains or refers to all relevant papers, which were developped during the last 7 years addressing the three Millennium problems: RH, NSE, YME. This journey ended up into a combined proposed mathematical solution framework: there is common Hilbert space based solution platform, avoiding e.g. gauge principles (quantum field theory), co-variant derivatives resp. differentiable manifolds (gravitation field theory) concepts and force type dependent quantum/quark types.
An application of the proposed distributional Hilbert
space framework is provided in the context of the non-linear Landau
damping phenomenon in plasma physics, where the standard mathematical
models are built on; more especially, this is about the Landau, Vlasov,
Poisson, Lorentz, Boltzmann PDE systems, which are purely classical PDE
systems and the corresponding existing proofs of the Landau damping
phenomenon for the linear and the nonlinear cases, are applying
classical techniques. In other words, an observed physical quantum
mechanics/dynamics phenomenon is proven based on classical mathematical
models and related proof techniques.
In section 1 of the following paper a high level
overview regarding the newly proposed quantum ("particles": bosons &
fermions) state and quantum energy model is provided. It is basically about a common distributional Hilbert space based model for quantum state & quantum mass/energy PDE systems. It enable a "fermions quantum state" Hilbert space H(0), which is dense in H(-1/2) with respect to the H(-1/2) norm, and its related (orthogonal) "bosons quantum state" Hilbert space H(-1/2)-H(0), which is a closed subspace of H(-1/2).