Fu-Xi Universal Nature Tunnel and Muskat interface Flow*

The Unitary Space-Time and its evolutions is the heart of the Generalized Newton's Laws (GNL). The Fu-Xi Universal Nature Tunnel is topological representation of the GNL. In this paper, using self-similar solutions for the Muskat Equation as an example, I prove that the Fu-Xi quantum tunnel is a unique nature orbit for Universe, Fundamental Particles and Life.

The Muskat equation is an important model in the analysis of free surface flows, which describes the dynamics of the interface separating two fluids whose velocities obey Darcy's law. Muskat problem is equivalent to the following equation:

∂_tf = ρ/(2π)pv ∫_R∂_x△_αf/(1 + (△_αf)²)dα ,    △_α f(x) = (f(x) - f(x-α))/α,    x ε R.

Most notably, an initial smooth interface can turn and later lose regularity in finite time. Thus, finding criteria for global existence became one of the main questions for the Muskat equation. Medium-size initial data in critical space but with uniformly continuous slope guarantees global well-posedness. It means that the finding exact analytical solutions and giving a unique orbit of interface, until today, are an important open problem of the Mathematics and the Physics ( from 1937, see M. Muskat, "The flow of homogeneous fluids through porous media"). 

Using topological quantum gravity CW complex (Cohomology and Homology with Singularity), I recovered all analytical performances and explicit evolution orbits, which is a similar unitary group theory with the Fu-Xi Complex Holography. I also obtain total 4 critical points with reflection motive.  

My main results include two parts: 

1. give all exact solutions of the Muskat equation;

2. present a unique quantum gravity orbit of the Muskat interface flow.

Finally, I show that Muskat interface orbit is an exact isomorphism of the Fu-Xi Holography.

As a by-product, I also critically prove that Nonlinear Ricci Flow Orbit is another isomorphism.

These results prove that the Generalized Newton's Laws theory have a robust and powerful mathematical base.