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Publications [#243847] of Jonathan C. Mattingly

Papers Published

1. Mattingly, JC, Ergodicity of $2$D Navier-Stokes equations with random forcing and large viscosity, Communications in Mathematical Physics, vol. 206 no. 2 (1999), pp. 273-288, Springer Nature, ISSN 0010-3616 [doi]
   (last updated on 2024/04/23)

   Abstract:
   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.