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Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$

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  • We consider finite energy solutions for the damped and driven two-dimensional Navier--Stokes equations in the plane and show that the corresponding dynamical system possesses a global attractor. We obtain upper bounds for its fractal dimension when the forcing term belongs to the whole scale of homogeneous Sobolev spaces from $-1$ to $1$.
    Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35Q30, 76D05.

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