Date: Thursday, January 17, 2013
Location: 4088 East Hall (4:00 PM to 5:00 PM)
Title: Holder Continuous Euler Flows with Compact Support in Time
Abstract: Motivated by the theory of hydrodynamic turbulence, Onsager
conjectured in 1949 that solutions to the incompressible Euler
equations with Holder regularity less than 1/3 may fail to conserve
energy. DeLellis and Szkelyhidi have pioneered an approach to
constructing such irregular flows based on an iteration scheme used by
Nash to construct "wild" C^1 isometric embeddings. 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 recent work on an improved
iteration scheme using nonlinear phase functions for the corrections,
which yields solutions in three dimensions with compact support in
time and Holder regularity below 1/5.
Speaker: Philip Isett
Institution: Princeton Univ.
Event Organizer:
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