- Series
- PDE Seminar
- Time
- Tuesday, March 3, 2015 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- skiles 006
- Speaker
- Phillip Isett – MIT
- Organizer
- Geng Chen
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.
De Lellis 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 1/5- as well as other recent results.