Enhanced dissipation by circularly symmetric and parallel pipe flows

We study enhanced dissipation due to the combined effect of diffusion or hyperdiffusion and advection by an incompressible flow with circular or cylindrical symmetry in 2 and 3 space dimensions, respectively. By using resolvent estimates for m-accretive operators (Wei, 2021), under a suitable condition on the velocity adapted from Gallay and Coti Zelati (2021), we establish enhanced dissipation for the advection-(hyper)diffusion equation and quantify it in terms of rates of decay in time for the solution, suitably projected, with an improved explicit dependence on the diffusivity. Our results extend prior results in Coti Zelati and Dolce (2020).