Matthew Novack, IAS

Abstract: We will discuss the motivation and techniques behind a recent construction of non-conservative weak solutions to the 3D incompressible Euler equations on the periodic box. The most important feature of this construction is that for any positive regularity parameter β < 1/2, it produces infinitely many solutions which lie in C^0_t H^β_x . In particular, these solutions have an L^2-based regularity index strictly larger than 1/3, thus deviating from the scaling of the Kolmogorov-Obhukov 5/3 power spectrum in the inertial range. This is joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol.