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

Alexei Ilyin; Kavita Patni; Sergey Zelik

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arXiv · 1503.03415

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

Alexei Ilyin·Kavita Patni·Sergey Zelik

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Abstract

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

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Alexei Ilyin, Kavita Patni, Sergey Zelik. 2015-03-11. Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$. https://arxiv.org/abs/1503.03415

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