The Maximum Principle of the Navier-Stokes Equation

Abstract

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.