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Статья

Strong trajectory and global W1,p-attractors for the damped-driven euler system in R2

Discrete and Continuous Dynamical Systems - Series B. 2017. Vol. 22. No. 5. P. 1835 -1855.
Chepyzhov V. V., Ilyin A., Zelik S.

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 H1. A similar result on the strong attraction holds in the spaces H1 ∪ {u: ∥ curl u ∥ Lp < ∞} for p ≥ 2.