| 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 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 of three-dimensional nonlinear dynamics. |
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