Abstract
AbstractIn this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius.
Publisher
Springer Science and Business Media LLC
Reference12 articles.
1. Albritton, D., Beekie, R., Novack, M.: Enhanced dissipation and Hörmander’s hypoellipticity. J. Funct. Anal. 283(3), 109522 (2022)
2. Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67–77 (1956)
3. Bedrossian, J., Coti Zelati, M.: Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows. Arch. Ration. Mech. Anal. 224(3), 1161–1204 (2017)
4. Bedrossian, J., Coti Zelati, M., Dolce, M.: Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space. arXiv:2211.05079 (2022)
5. Constantin, P., Kiselev, A., Ryzhik, L., Zlatoš, A.: Diffusion and mixing in fluid flow. Ann. Math. (2) 168(2), 643–674 (2008)