Analysis Seminar

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Stability of negative regularity mixing and applications

Speaker: Patrick Flynn, Yale University

Location: Warren Weaver Hall 1302

Date: Thursday, October 15, 2026, 11 a.m.

Synopsis:

In joint work with Antonio Agresti and Bill Cooperman, we consider the mixing of scalar quantities advected by random vector fields, such as solutions to stochastic fluid equations. We show that the property of negative regularity mixing is stable under perturbations of the joint process of the scalar and the underlying vector field. We give three applications: first, we prove enhanced dissipation for the corresponding advection diffusion equation. Second, we prove negative regularity mixing of active scalars, that is, when the underlying stochastic fluid equation is coupled to the scalar through a forcing term. Third, we show low regularity mixing for fluid equations with smooth random forcing.