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Upper bound on the dimension of the attractor for nonhomogeneous Navier-Stokes equations. (English) Zbl 0949.35112
Summary: Our aim 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 attactor of the form \(c\text{Re}^{3/2}\), where Re is the Reynolds number. This improves significantly on previous bounds which were exponential in Re.

MSC:
35Q30 Navier-Stokes equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B40 Asymptotic behavior of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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