Massimo Sorella (Lausanne): Enhanced dissipation for non-degenerate elliptic points

We study dissipation enhancing properties of the advection-diffusion equation advected by a class of Hamiltonian flows with a non-degenerate elliptic point which are quantitatively close to radial flows. Namely, we aim at establishing a convergence towards the streamline average on sub-diffusive timescales. The precise timescale is given as a function of the asymptotic behaviour of the period function. In particular, we recover the enhanced dissipation rates for radial flows. Our proof is based on spectral techniques applied to a model problem (for which we can consider more general Hamiltonian flows such as the cellular flow). This is a joint work with M. Dolce and C. Johansson.