Joint BCAM-UPV/EHU Analysis and PDE seminar: Hölder continuous turbulent weak solutions of the incompressible Euler equations

Abstract
In this talk I will give a general overview on the available results for Hölder continuous wild weak solutions of the incompressible Euler equations. Starting from the celebrated Onsager's conjecture I will explain how some deep regularity of the kinetic energy can be derived even in the range in which it is not necessarily conserved. This is linked to a conjecture by Isett and Oh from 2016, which we recently proved to be true in a joint work with Riccardo Tione, and also to the construction of wild weak solutions of Euler that are smooth outside a set of singular times of quantifiable Hausdorff dimension. The latter is a forthcoming joint work with Silja Haffter in which we also state a conjecture on what the sharp Hausdorff dimension of the singular set of such turbulent solutions could be.

Link to the session: https://zoom.us/j/91533421483?pwd=YyttaTNpV0E0QlRXNlZDazJEM2FJZz09

More info at https://sites.google.com/view/apdebilbao/home