Some Results for the Primitive Equations with Physical Boundary Conditions

Details Some Results for the Primitive Equations with Physical Boundary Conditions Some Results for the Primitive Equations with Physical Boundary Conditions

2011-11-04

arxiv.org/abs/1111.1245v1

Physics

Mathematical Physics

Scientific paper

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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