Upper bounds for the attractor dimension of damped Navier-Stokes\n equations in mathbb R²

2015/03/11 by Alexei Ilyin, Ilyin, Alexei, Kavita Patni +3
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1503.03415

Abstract

We consider finite energy solutions for the damped and driven two-dimensional\nNavier--Stokes equations in the plane and show that the corresponding dynamical\nsystem possesses a global attractor. We obtain upper bounds for its fractal\ndimension when the forcing term belongs to the whole scale of homogeneous\nSobolev spaces from -1 to 1\n

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