Communications on Pure and Applied Mathematics · 2001 · 136 citations · 13 references
Natural SciencesMathematicsMechanical EngineeringComputational Fluid DynamicsFluid DynamicsStochastic ProcessesDissipative SystemsErgodic TheoryNavier-stokes EquationsStochastic Differential EquationsErgodic ProcessesErgodic PropertiesErgodicityGalerkin ApproximationGalerkin DiscretizationStochastic FlowsStochastic Nonlinear DynamicsStochastic Partial Differential Equations
Abstract We study Galerkin truncations of the two‐dimensional Navier‐Stokes equation under degenerate, large‐scale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. Our results rely heavily on the structure of the nonlinearity. © 2001 John Wiley & Sons, Inc.
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