Antoine Remond-Tiedrez : Onsager's conjecture
Channel: Grad Student
Date: 2018-03-21

Classical (i.e. smooth) solutions of the 3D incompressible Euler equations preserve kinetic energy. This is no longer true for weak (i.e. merely square-integrable) solutions, and so naturally one seeks the critical degree of regularity at which this transition between conservative and non-conservative solutions occurs. Onsager conjectured the critical regularity to be Holder with exponent 1/3. This conjecture was recently resolved in the affirmative, and is a good reminder that choosing the right function space in PDE is not just a technical matter, all the while teaching us something new about the Euler equations, a most venerable PDE. I will discuss the proof of one direction of this conjecture, and (time-permitting) will discuss elements of the proof of the other (more recent, and much trickier!) direction.