Wednesday, September 21, 2016 at 3:00 PM in SAS 4201
Alex Mahalov, Arizona State
Stochastic Three-Dimensional Rotating Navier-Stokes Equations: Averaging, Convergence and Regularity
We consider stochastic three-dimensional rotating Navier-Stokes equations and prove averaging theorems for stochastic problems in the case of strong rotation. Regularity results are established by bootstrapping from global regularity of the limit stochastic equations and convergence theorems. 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 a precise mechanism of relevant three-dimensional nonlinear interactions. We establish multiscale averaging and convergence theorems for the stochastic dynamics. References  Flandoli F. , Mahalov A. , Stochastic 3D Rotating Navier-Stokes Equations: Averaging, Convergence and Regularity, Archive for Rational Mechanics and Analysis, 205, No. 1, 195237 (2012).  Cheng B. , Mahalov A. , Euler Equations on a Fast Rotating Sphere Time- Averages and Zonal Flows, European Journal of Mechanics B/Fluids, 37, 48-58 (2013).  Mahalov A. Multiscale modeling and nested simulations of three-dimensional ionospheric plasmas: Rayleigh-Taylor turbulence and nonequilibrium layer dynamics at fine scales, Physica Scripta, Phys. Scr. 89 (2014) 098001 (22pp), Royal Swedish Academy of Sciences.
Wednesday, September 28, 2016 at 3:00 PM in SAS 4201
Khai Nguyen, NC State Mathematics
Compactness estimate for some nonlinear PDEs
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