Nonlinear Partial Differential Equations

Date: October 31, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Alex Mahalov, Arizona State University

Title: Nonlinear PDE's seminar

Abstract:

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

Abstract:
We consider stochastic three-dimensional Navier-Stokes equations + Waves on long time intervals. 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. 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.