Ergodicity of 2D Navier–Stokes Equations with¶Random Forcing and Large Viscosity
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The stochastically forced, two-dimensional, incompressable Navier–Stokes equations are shown to possess an unique invariant measure if the viscosity is taken large enough. This result follows from a stronger result showing that at high viscosity there is a unique stationary solution which attracts solutions started from arbitrary initial conditions. That is to say, the system has a trivial random attractor. Along the way, results controling the expectation and averaging time of the energy and enstrophy are given.
KeywordsViscosity Stationary Solution Stokes Equation Invariant Measure High Viscosity
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