[Vasseur, 2016] The De Giorgi Method for Elliptic and Parabolic Equations and Some Applications
[Caffarelli, Vasseur, 2010] The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics
These lecture notes describe the De Giorgi method in detail. They give a great background for this paper:
[Vasseur, 2007] A new proof of partial regularity of solutions to Navier-Stokes equations
The original proof of partial regularity of solutions to Navier-Stokes is contained in these papers:
[Caffarelli, Kohn, Nirenberg, 1982] Partial Regularity of Suitable Weak Solutions of the Navier-Stokes Equations
Papers related to Onsager’s conjecture and convex integration.
[Constantin, Weinan, Titi, 1993] Onsager’s Conjecture on the Energy Conservation for Solutions of Euler’s Equation
[Isett, 2016] A Proof of Onsager’s Conjecture
[De Lellis, Szekelyhidi, 2019] On Turbulence and Geometry: from Nash to Onsager
A Stochastic-Lagrangian viewpoint of Navier-Stokes:
[Constantin, Iyer, 2011] A Stochastic-Lagrangian Approach to the Navier-Stokes Equations in Domains with Boundary
[Constantin, Iyer, 2008] A stochastic Lagrangian representation of the three dimensional incompressible Navier–Stokes equations.
The translated K41 paper:
[Kolmogorov, 1941] The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers