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Global \(\varphi\)-attractor for a modified 3D Bénard system on channel-like domains. (English) Zbl 1288.35081

Summary: In this paper we prove the existence of a global \(\varphi\)-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35K55 Nonlinear parabolic equations
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
37B25 Stability of topological dynamical systems
58C06 Set-valued and function-space-valued mappings on manifolds
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