The Maximum Principle of the Navier-Stokes Equation

TL;DR

This paper establishes a maximum principle for the Navier-Stokes equations by deriving a related nonlinear parabolic equation for kinetic energy density, leading to proofs of unique solvability and existence of solutions.

Contribution

It introduces a maximum principle for the Navier-Stokes equations and proves the existence and uniqueness of solutions based on this property.

Findings

Maximum principle for the Navier-Stokes equation established

Unique solvability of weak solutions proved

Existence of strong solutions demonstrated

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.