The Solution of the 3 Dimensional Navier-Stokes Momentum Equations (A 3 Dimensional Integral Equation Approach)

This paper provides the solution of the classical navier stokes mo-mentum equations within the common three dimensional euclidean space. The function variable of the equations, h := (p, v) takes values in R4, consisting of a skalar field ”pressure” p and a vector field ”velocity” v where both, p and v depend on the same four variables (x, y, z, t). The solution space L ⊂ {h ∈ C(R4 , R4 ), the continuous differentiable functions from R4 to R4 |v(x, y, z, t) = h(·, w(x, y, z, t)) ∈ C 2
(R4 , R3 ), the twice continuous differentiable functions from R4to R3  , for all functions w}. The equation system ”navier-stokes”, as we will show, is underspecified as infinite many solutions exist. We will show smoothness and existence of the general solution of the navier stokes equations. We will deal with fluid dynamics and their boundary conditions for the com- pressible case as a general case of the incompressible one.