Strong trajectory attractors for dissipative Euler equations

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Abstract

The 2D Euler equations with periodic boundary conditions and extra linear dissipative term Ru, R>0 are considered and the existence of a strong trajectory attractor in the space Lloc∞(R{double-struck}+,H1) is established under the assumption that the external forces have bounded vorticity. This result is obtained by proving that any solution belonging the proper weak trajectory attractor has a bounded vorticity which implies its uniqueness (due to the Yudovich theorem) and allows to verify the validity of the energy equality on the weak attractor. The convergence to the attractor in the strong topology is then proved via the energy method. © 2011 Elsevier Masson SAS.

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Chepyzhov, V. V., Vishik, M. I., & Zelik, S. V. (2011). Strong trajectory attractors for dissipative Euler equations. Journal Des Mathematiques Pures et Appliquees, 96(4), 395–407. https://doi.org/10.1016/j.matpur.2011.04.007

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