Well-posedness of rough 2D Euler equations with bounded vorticity

In this talk, we consider the 2D Euler equations with bounded initial vorticity and perturbed by rough transport noise. We show that a unique solution exists, which coincides with the starting condition advected by the Lagrangian flow. Moreover, we prove that the solution map is continuous with respect to the initial vorticity, the advecting vector fields and the rough perturbation. As an immediate corollary, we obtain a Wong-Zakai result for fractional Brownian driving paths.
This talk is based on a joint work with Leonardo Roveri.