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

  • * Corresponding author: V. Chepyzhov

    * Corresponding author: V. Chepyzhov 
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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 $H^1\cap\{u:\ \|\text{curl}\, u\|_{L^p}<∞\}$ for $p≥2$ .

    Mathematics Subject Classification: Primary:35B40, 35B41;Secondary:35Q35.


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