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The dependence of the fractal dimension of global attractors for the damped3D Euler--Bardina equations on the regularization parameter $\alpha>0$ andEkman damping coefficient $\gamma>0$ is studied. We present explicit upperbounds for this dimension for the case of the whole space, periodic boundaryconditions, and the case of bounded domain with Dirichlet boundary conditions.The sharpness of these estimates when $\alpha\to0$ and $\gamma\to0$ (whichcorresponds in the limit to the classical Euler equations) is demonstrated onthe 3D Kolmogorov flows on a torus.

Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations