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Graduate Seminar
Antoine RemondTiedrez CMU Title: Onsager's conjecture Abstract: Classical (i.e. smooth) solutions of the 3D incompressible Euler equations preserve kinetic energy. This is no longer true for weak (i.e. merely squareintegrable) solutions, and so naturally one seeks the critical degree of regularity at which this transition between conservative and nonconservative 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 (timepermitting) will discuss elements of the proof of the other (more recent, and much trickier!) direction. Date: Tuesday, March 20, 2018 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Son Van 