Bounded Energy on Compressible Fluid Dynamics and Plasma Physics with Air/Gas Flow

Let (x, t) and p(x, t) be a velocity vector and pressure illustrated on some fluid. Then, there exists new concepts possibly applicable to various fields. These new ideas will be presented as derivation from previously developed mathematical concepts. The new rules are Partial Integrating Factors, Partial Integration by Parts and Partial Integration with Exponentials. The goal of this paper is to define a velocity vector field over some liquid or gas.