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arXiv · 1808.09683

Attractor Dimensions of Three-Dimensional Navier-Stokes-$\alpha$ Model for Fast Rotating Fluids on Generic-Period Domains: Comparison with Navier-Stokes Equations

Bong-Sik Kim
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Abstract

The three-dimensional Navier-Stokes-$\alpha$ model for fast rotating geophysical fluids is considered. The Navier-Stokes-$\alpha$ model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as $\alpha\rightarrow 0^+$. We estimate upper bounds for the dimensions of global attractors and study the dependence of the dimensions on the parameter $\alpha$. All the estimates are uniform in $\alpha$, and our estimate of attractor dimensions remain finite when $\alpha\rightarrow 0^+$.

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Bong-Sik Kim. 2018-08-29. Attractor Dimensions of Three-Dimensional Navier-Stokes-$\alpha$ Model for Fast Rotating Fluids on Generic-Period Domains: Comparison with Navier-Stokes Equations. https://arxiv.org/abs/1808.09683

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