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Effects of Mixing Flows on Aggregative Behavior

Effects of Mixing Flows on Aggregative Behavior

Start: 
Monday, May 6, 2024 12:00 pm
End: 
Monday, May 6, 2024 1:00 pm
Location: 
Kidder 237
Nicholas Harrison
Oregon State University

In this talk, I'll consider the scenario described by the Patlak-Keller-Segel (PKS) Model of chemotactic aggregation together with the presence of some strong ambient advective forcing fluid, say wind or turbulent waters. The PKS model is well-known to exhibit finite-time blow-up behavior in many relevant settings, but it turns out that if the advective flow is sufficiently well-mixing, then there is a regularization effect which suppresses this blow-up (and in fact induces convergence to the mean). I'll discuss an analytic measure of mixing, introduce what are known as Relaxation Enhancing (RE) flows, and how RE flows can suppress the blow-up described as above in the parabolic-elliptic PKS Model. If there is time, I'll pose the question of "anomalous" blow-up suppression in the case of the zero diffusivity limit to the hyperbolic-elliptic PKS, for which there appears to be many similarities with recent results around scalar turbulence.

Contact: 
Xueying Yu