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arXiv · 1703.05538

Long-time behavior of the three dimensional globally modified Navier-Stokes equations

Fang Li·Bo You
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Abstract

This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\mathcal{A}_0$ in $H$ and investigate the regularity of the global attractors by proving that $\mathcal{A}_0=\mathcal{A}$ established in \cite{ct}, which implies the asymptotic smoothing effect of solutions for the three dimensional globally modified Navier-Stokes equations in the sense that the solutions will eventually become more regular than the initial data. Furthermore, we construct an exponential attractor in $H$ by verifying the smooth property of the difference of two solutions, which entails the fractal dimension of the global attractor is finite.

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Fang Li, Bo You. 2017-03-16. Long-time behavior of the three dimensional globally modified Navier-Stokes equations. https://arxiv.org/abs/1703.05538

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