Department of Mathematics

Analysis and PDE

  •  Stochastic Three-Dimensional Rotating Navier-Stokes Equations:  Averaging, Convergence and Regularity 
  •  10/24/2016
  •  4:02 PM - 5:00 PM
  •  C517 Wells Hall
  •  Alex Mahalov, Arizona State University

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 [1] Flandoli F. , Mahalov A. , “Stochastic 3D Rotating Navier-Stokes Equations: Averaging, Convergence and Regularity,” Archive for Rational Mechanics and Analysis, 205, No. 1, 195–237 (2012). [2] 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). [3] 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.

 

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Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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