Abstract
In this paper, we consider the (simplified) 3-dimensional primitive equations with physical boundary conditions. We show that the equations with constant forcing have a bounded absorbing ball in the H 1-norm and that a solution to the unforced equations has its H 1-norm decay to 0. From this, we argue that there exists an invariant measure (on H 1) for the equations under random kick-forcing.
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Evans, L.C., Gastler, R. Some results for the primitive equations with physical boundary conditions. Z. Angew. Math. Phys. 64, 1729–1744 (2013). https://doi.org/10.1007/s00033-013-0320-6
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DOI: https://doi.org/10.1007/s00033-013-0320-6