Communications in Mathematical Physics

, Volume 206, Issue 2, pp 273–288 | Cite as

Ergodicity of 2D Navier–Stokes Equations with¶Random Forcing and Large Viscosity

  • Jonathan C.  Mattingly


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.


Viscosity Stationary Solution Stokes Equation Invariant Measure High Viscosity 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jonathan C.  Mattingly
    • 1
  1. 1.Program in Applied and Computational Mathematics, Princeton NJ, USAUS

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