Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Results for the Primitive Equations with Physical Boundary
  Conditions   In this paper we consider the (simplified) 3-dimensional primitive equations
with \emph{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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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess