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Strong trajectory attractors for dissipative Euler equations. (English) Zbl 1230.35092

Authors’ abstract: The two-dimensional Euler equations with periodic boundary conditions and extra linear dissipative term are considered and the existence of a strong trajectory attractor 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 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.

MSC:

35Q31 Euler equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35B41 Attractors
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