Patrick Flynn, UCLA

Title: Negative regularity mixing of passive scalars in stochastic fluid mechanics

Abstract: Consider a passive scalar advected by a random vector field on a compact manifold, such as the solution to the 2D stochastic Navier-Stokes equation on a periodic box. In this talk, I discuss my work with J. Bedrossian and S. Punshon-Smith, where we show that if the passive scalar is initially in some negative regularity Sobolev space, then it will decay exponentially in the same space (in expectation). We prove this result using techniques from dynamical systems theory and semiclassical analysis. Going forward, we hope to apply this result to the problem of turbulence.