Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

V. V. Chepyzhov; A. A. Ilyin; S. V. Zelik

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arXiv · 1511.03873

Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

V. V. Chepyzhov·A. A. Ilyin·S. V. Zelik

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Abstract

We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space $H^1$. A similar result on the strong attraction holds in the spaces $H^1\cap\{u:\ \|\mathrm{curl} u\|_{L^p}<\infty\}$ for $p\ge2$.

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V. V. Chepyzhov, A. A. Ilyin, S. V. Zelik. 2015-11-12. Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$. https://arxiv.org/abs/1511.03873

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