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Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$
2017
Discrete and continuous dynamical systems. Series B
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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 ∩ {u : curl u L p < ∞} for p ≥ 2. 2010 Mathematics Subject Classification. Primary: 35B40,
doi:10.3934/dcdsb.2017109
fatcat:fyrf3tktlrazrmlh4v6k3mo7c4