Application of Onsager's Variational Principle to the Navier-Stokes Equations

In this note we propose a basic $L^2$-based approach for studying the global and local energy equalities of the incompressible 3D Navier-Stokes equations in the standard energy class on $\mathbb{T}^3 \times (0,T]$. Motivated by L. Onsager's principle of least dissipation of energy (1931), we give a