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Probability and Computational Finance Seminar
Jingyu Huang University of Utah Title: Analysis of a Kraichnan-type Fluid Model Abstract: We study the turbulent transport of a passive scalar quantity in a stratified, 2-D random velocity field. It is described by the stochastic partial differential equation$\partial_t \theta(t,x,y)=\nu \Delta \theta(t,x,y)+V(t,x)\partial_y \theta (t,x,y)$ for $t\geq 0, x,y,\in{\mathbb R}$where V is some Gaussian noise. We show via a priori bounds that, typically, the solution decays with time. More interesting still, the decay is shown to be macroscopically multifractal in special settings. The detailed analysis is based on a probabilistic representation of the solution, which is likely to have other applications as well. This is based on joint work with Davar Khoshnevisan. Date: Monday, October 16, 2017 Time: 4:30 pm Location: Wean Hall 8220 Submitted by: Steve Shreve |