  In the work of Navier-Stokes (NSE) equation, derived a nonlinear parabolic
equation for kinetic energy density, and identified an important property of
this equation - the maximum principle. The latter shows the validity of the
maximum principle and the NSE. On the basis of what, the unique solvability of
the weak and the existence of strong solutions for NSE was proved wholly in
time t \in [0, T], \forall T < \infty.
