TY - JOUR
T1 - Enhanced dissipation by circularly symmetric and parallel pipe flows
AU - Feng, Yuanyuan
AU - Mazzucato, Anna L.
AU - Nobili, Camilla
N1 - Funding Information:
The authors would like to thank Michele Coti Zelati and Gautam Iyer for useful discussions.Y. Feng was supported by Science and Technology Commission of Shanghai Municipality (STCSM), China under Grant No. 22DZ2229014 . A. Mazzucato was partially supported by the US National Science Foundation under grants DMS-1909103 and DMS-2206453 . C. Nobili was partially supported by the DFG, Germany - TRR181 and the DFG, Germany - GrK2583 . The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, for support and hospitality during the programme, Mathematical aspects of turbulence: where do we stand?, where work on this paper was partially undertaken. The work of the Institute is supported by EPSRC, United Kingdom Grant No EP/R014604/1 .
Publisher Copyright:
© 2022 The Author(s)
PY - 2023/3
Y1 - 2023/3
N2 - 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).
AB - 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).
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U2 - 10.1016/j.physd.2022.133640
DO - 10.1016/j.physd.2022.133640
M3 - Review article
AN - SCOPUS:85145778558
SN - 0167-2789
VL - 445
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 133640
ER -