Abstract
In this paper, we first present a Gearhart-Prüss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) we give a simple proof of the result proved by Constantin et al. on relaxation enhancement induced by incompressible flows; (2) we show that shear flows with a class of Weierstrass functions obey logarithmically fast dissipation time-scales.
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Acknowledgements
This work was supported by China Postdoctoral Science Foundation (Grant No. 2018M 630016). The author thanks Professor Zhifei Zhang for many helpful suggestions.
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Wei, D. Diffusion and mixing in fluid flow via the resolvent estimate. Sci. China Math. 64, 507–518 (2021). https://doi.org/10.1007/s11425-018-9461-8
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DOI: https://doi.org/10.1007/s11425-018-9461-8