Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise

Details Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise

2002-10-05

arxiv.org/abs/math/0210082v1

Mathematics

Probability

Scientific paper

We prove ergodicity of the finite dimensional approximations of the three
dimensional Navier-Stokes equations, driven by a random force. The forcing
noise acts only on a few modes and some algebraic conditions on the forced
modes are found that imply the ergodicity. The convergence rate to the unique
invariant measure is shown to be exponential.

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