Characteristic exponents for a viscous fluid subjected to time dependent forces

We consider a viscous incompressible fluid enclosed in a bounded region of ℝ2 or ℝ3, and subjected to time dependent forces. Using bound state estimates for the Schrödinger operator, we obtain rigorous bounds for the characteristic exponents, entropy (Kolmogorov-Sinai invariant), and Hausdorff dimension of attracting sets. Our methods are of potential use for more general time evolutions described by nonlinear partial differential equations.

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