Diffusion and mixing in fluid flow via the resolvent estimate

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.

arXiv comment12 pages

References in corpus (3)

• Transition threshold for the 3D Couette flow in Sobolev space
• From resolvent bounds to semigroup bounds
• Linear inviscid damping and enhanced dissipation for the Kolmogorov flow

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