Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics

Department of Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Stephanie Zerby, Wen-Ching W. Li.

Speaker: Alex Mahalov, Arizona State University

Abstract: We consider stochastic three-dimensional Navier-Stokes equations + Waves. Regularity results are established by bootstrapping from global regularity of the averaged stochastic resonant equations and convergence theorems. The averaged covariance operator couples stochastic and wave effects. The energy injected in the system by the noise is large, the initial condition has large energy, and the regularization time horizon is long. Infinite time regularity is proven for the deterministic case. Regularization is the consequence of precise mechanisms of relevant three-dimensional nonlinear interactions. We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework. We also present theoretical and computational results for three-dimensional nonlinear dynamics.

Room Reservation Information

Room Number: 114 McAllister

Date: 04/25/2019

Time: 3:30pm - 4:30pm