Proof of the 3D Navier-Stokes equation's global existence and smoothness of solutions – Applying a new analytical approach with certain boundary conditions

The Navier-Stokes equations are mainly useful for describing the relationship between velocity, pressure and density of moving fluid. In the beginning of the 19th century, these partial differential equations for modeling fluid dynamics are discovered independently from each other by French and Irish physicists Claude-Louis Navier and George Gabriel Stokes. The main focus of this research paper is to discover if and under which circumstances globally defined and smooth solutions to the 3-dimensional Navier-Stokes PDEs could exist. By using an entire and exclusive analytical approach, it could be shown that under certain predefined boundary conditions and given any initial conditions, there exist solutions to the 3D Navier-Stokes equations which are indeed globally defined and smooth.