 96342 Peter Constantin, Jiahong Wu
 Statistical Solutions of the NavierStokes Equations on the Phase Space of
Vorticity and the Inviscid Limits
(42K, Latex)
Jul 22, 96

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Abstract. Using the methods of Foias \cite{Fo} and VishikFursikov \cite{VF}, we prove
the existence and uniqueness of both spatial and spacetime statistical
solutions of the NavierStokes equations on the phase space of vorticity.
Here the initial vorticity is in Yudovich space and the initial measure
has finite mean enstrophy. We show under further assumptions on the
initial vorticity that the statistical solutions of the NavierStokes
equations converge weakly and the inviscid limits are the corresponding
statistical solutions of the Euler equations.
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