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Article Contents

# Upper bound on the dimension of the attractor for nonhomogeneous Navier-Stokes equations

• Our aim in this article is to derive an upper bound on the dimension of the attractor for Navier-Stokes equations with nonhomogeneous boundary conditions. In space dimension two, for flows in general domains with prescribed tangential velocity at the boundary, we obtain a bound on the dimension of the attractor of the form $c\mathcal{R} e^{3/2}$, where $\mathcal{R} e$ is the Reynolds number. This improves significantly on previous bounds which were exponential in $\mathcal{R} e$.
Mathematics Subject Classification: 35B30, 35B40, 35Q30, 76D05, 76F10, 76F20, 58F39, 58F13, 28A78, 28A80.

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