The Solution of the 3 Dimensional Navier-Stokes Momentum Equations (A 3 Dimensional Integral Equation Approach) (London Journal of Engineering Research, 2024)
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.
Keywords: pirate attacks; risk analysis; K-means clustering; Autoencoder; EWM-TOPSIS; Compressive Strength; tensile strength; mechanical properties; compressed earth blocks (CEBs); eggshell waste; lime; Finite Element Analysis (FEA); Carbon Nanotubes (CNT); Liquid Oxygen (LOX); Liquid Hydrogen (LH2); External Fuel Tank (EFT).; Fluid dynamics; Claude-Luis Navier and George Gabriel Stokes; 3- dimensional Navier-Stokes equations; Compressible and incom pressible fluids; Differential geometry and analysis