Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Dr. Tommaso Rosati - University of Warwick

Abstract: We prove global in time well-posedness for perturbations of the 2D Navier-Stokes equations driven by a perturbation of additive space-time white noise. The proof relies on a dynamic high-low frequency decomposition, tools from paracontrolled calculus and an L2 energy estimate for low frequencies. Our argument requires the solution to the linear equation to be a log-correlated field. We do not rely on (or have) explicit knowledge of the invariant measure: the perturbation is not restricted to the Cameron–Martin space of the noise. Our approach allows for anticipative and critical (L2) initial data. Time permitting, we will discuss related results for scalar conservations laws.

Joint work with Martin Hairer and (in progress) Ana Djurdjevac