h-principle for the incompressible Euler equations

Antoine Choffrut

Thursday 29th November, 2012 14:00-15:00 325

Abstract

Recently, De Lellis & Szekelyhidi have made significant progress towards proving the Onsager conjecture. Indeed, they constructed energy dissipative solutions to the incompressible Euler equations on the three-dimensional torus, and with Hoelder exponent smaller than 1/10. I will present a density result ("h-principle") associated with this construction, in the two- and three-dimensional torus. Namely, I identify the largest set of "subsolutions" which can be arbitrarily accurately approximated (in the sup-norm) by exact solutions with Hoelder exponent smaller than <1/10.

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