Diffusion and mixing in fluid flow via the resolvent estimate
arXiv:1811.11904 · doi:10.1007/s11425-018-9461-8
Abstract
In this paper, we first present a Gearhardt-Prüss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement induced by incompressible flows; (2) show that shear flows with a class of Weierstrass functions obey logarithmically fast dissipation time-scales.
12 pages