Ed Waymire (OSU): Stochastic Cascades and Mean Flow Equations

A rich class of multiplicative cascades will be introduced extending that of Yves Le Jan and Alain-Sol Sznitman (1997) for (deterministic) 3d incompressible Navier-Stokes flow.  The extension accommodates a larger class of mean flows that include fractional Navier-Stokes flow, Montgomery-Smith flow, and Aldous-Shields-Athreya flow, Burgers equation, the pantograph equation and more.  The mathematical framework and the roles of various statistical critical phenomena in the analysis of well-posedness of the mean flow will be described and illustrated by examples.  This is based on joint work with Radu Dascaliuc (OSU), Tuan Pham (BYU-Hawaii), and Enrique Thomann (OSU).