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Ergodicity for the Dissipative Boussinesq Equations with Random Forcing

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Abstract

We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, 440–746, Suwon, Korea

    Jihoon Lee

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544

    Ming-Yih Wu

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  1. Jihoon Lee
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  2. Ming-Yih Wu
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Correspondence to Jihoon Lee.

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Lee, J., Wu, MY. Ergodicity for the Dissipative Boussinesq Equations with Random Forcing. J Stat Phys 117, 929–973 (2004). https://doi.org/10.1007/s10955-004-5711-9

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  • DOI: https://doi.org/10.1007/s10955-004-5711-9

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