An Elementary Solution of the Navier-Stokes Existence and Smoothness: Very Weak Solutions

This is an application of the functional analysis. There are no long or complicated calculations, semi-groups or apriori estimates or boundary conditions are not used at all. Our very weak solutions do not satisfy energy inequality, but our solutions are unique, smooth, and the map <i>f→u </i>is continuous. The existence and the uniqueness follow similar to the proof of Banach's fixed point theorem.