数学科学研究所
Insitute of Mathematical Science

Colloquium: A quantitative relationship between mixing and enhanced dissipation

Colloquium | Institute of Mathematical Sciences

Time10:30-11:30, Feb 27th, Wednesday 

Location:Room 302, Library


Speaker: Dr. Matias Delgadino, Imperial College in London
Abstract:
We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequencies. When diffusion is present, mixing enhances the dissipative forces. This phenomenon is referred to as enhanced dissipation, namely the identification of a time-scale faster than the purely diffusive one. We establish a precise connection between quantitative mixing rates in terms of decay of negative Sobolev norms and enhanced dissipation time-scales. We will give a general overview on the subject, and present a few specific applications that include passive scalar evolution in both planar and radial settings, fractional diffusion, linearized two-dimensional Navier-Stokes equations, and even simple examples in kinetic theory.


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