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Forward Attraction of Nonautonomous Dynamical Systems and Applications to Navier-Stokes Equations

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Autor(es):
Cui, Hongyong ; Figueroa-Lopez, Rodiak N. ; Langa, Jose A. ; Nascimento, Marcelo J. D.
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 23, n. 3, p. 37-pg., 2024-01-01.
Resumo

In this paper we studied the forward dynamics of nonautonomous dynamical systems in terms of forward attractors. We first reviewed the well-known uniform attractor theory, and then by weakening the uniformity of attraction we introduced semiuniform forward attractors and minimal (nonuniform) forward attractors. With these semiuniform attractors, a characterization of the structure of uniform attractors was given: a uniform attractor is composed of two semiuniform attractors and bounded complete trajectories connecting them. As a consequence, the nature of the forward attraction of a dissipative nonautonomous dynamical system was then revealed: the vector field in the distant future of the system determines the (nonuniform) forward asymptotic behavior. A criterion for certain semiuniform attractors to have finite fractal dimension was given and the finite dimensionality of uniform attractors was discussed. Forward attracting time-dependent sets were studied also. A sufficient condition and a necessary condition for a time-dependent set to be forward attracting were given with illustrative counterexamples. Forward attractors of a Navier-Stokes equation with asymptotically vanishing viscosity (with an Euler equation as the limit equation) and with time-dependent forcing were studied as applications. (AU)

Processo FAPESP: 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação
Beneficiário:Alexandre Nolasco de Carvalho
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 22/16305-4 - Dinâmica assintótica de problemas semilineares
Beneficiário:Marcelo José Dias Nascimento
Modalidade de apoio: Auxílio à Pesquisa - Regular