UC Davis Mathematics

Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Recent progress towards Onsager's Conjecture

PDE and Applied Math Seminar

Speaker: Philip Isett, MIT
Location: 3106 MSB
Start time: Thu, Apr 17 2014, 4:10PM

Motivated by the theory of hydrodynamic turbulence, L. Onsager conjectured in 1949 that solutions to the incompressible Euler equations with Holder regularity less than 1/3 may fail to conserve energy. C. DeLellis and L. Székelyhidi, Jr. have pioneered an approach to constructing such irregular flows based on an iteration scheme known as convex integration. This approach involves correcting "approximate solutions" by adding rapid oscillations which are designed to reduce the error term in solving the equation. In this talk, I will discuss an improved convex integration framework, which yields solutions with Holder regularity as much as 1/5-.