Differential Equations: Determining Partial Integrability of Wave Theory

Abstract

Let’s put ourselves on a boat and watch waves travel behind it. The same concept can apply to air flow when traveling on an air plane. Previously and currently, mathematicians believe the wave mechanics and air flow is explained through a thorough understanding of existing solutions to Navier-Stokes equations. Since the nineteenth century, the understanding of these equations are unsubstantial. The goal is to create substantial qualitative input towards generating a mathematical theory unlocking implicit information within the Navier-Stokes equations. The literature will contain mathematical physical methods for locating closed general solutions applied to various fields.