Exponential mixing by shear flows

William Cooperman, Courant Institute
Fine Hall 314

Given a divergence-free vector field on the torus, we consider the mixing properties of the associated flow. There is a rich body of work studying the dependence of the mixing scale on various norms of the vector field. We will discuss some examples of particularly simple vector fields that mix at the optimal rate, and an improved lower bound on the mixing scale under the extra assumption that the vector field is a shear at each time.