Fluid Mechanics – Spring, 2019

[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

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