Trajectory attractors for dissipative 2D Euler and Navier-Stokes equations |
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Authors: | V V Chepyzhov M I Vishik |
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Institution: | (1) Institute for Information Transmission Problems, RAS (Kharkevich Institute), Bolshoy Karetnyi 19, Moscow, 127994, Russia |
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Abstract: | A trajectory attractor is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor, . Such systems model large-scale geophysical processes in atmosphere and ocean (see 1]). We prove that → as v → 0+ in the corresponding metric space. Moreover, we establish the existence of the minimal limit of the trajectory attractors as v → 0+. We prove that is a connected invariant subset of . The connectedness problem for the trajectory attractor by itself remains open.
Dedicated to the memory of Leonid Volevich
Partially supported by the Russian Foundation for Basic Research (projects no 08-01-00784 and 07-01-00500). The first author
has been partially supported by a research grant from the Caprio Foundation, Landau Network-Cento Volta. |
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