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Multi-valued dynamical systems on time-dependent metric spaces with applications to Navier-Stokes equations

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Autor(es):
Cui, Hongyong ; Lopez, Rodiak Nicolai Figueroa ; Lopez-Lazaro, Heraclio Ledgar ; Simsen, Jacson
Número total de Autores: 4
Tipo de documento: Artigo Científico
Fonte: MATHEMATISCHE ANNALEN; v. 390, n. 4, p. 56-pg., 2024-06-14.
Resumo

In this paper, we develop an extension of the theoretical framework of multi-valued dynamical systems for families of time-dependent phase spaces, where special attention was paid to the relationship between the pullback attractors of homeomorphically equivalent dynamical systems. We apply this theory to show that the 3D Navier-Stokes equations defined on a non-cylindrical domain, satisfying certain hypotheses about the energy inequality, generate an upper-semicontinuous multi-valued dynamical system, and then, by means of the energy method, we show that this system is asymptotically compact and has a pullback attractor on a tempered universe. Using current techniques we also prove that pullback attractors associated with the single-valued dynamical systems that satisfy the smoothing property have finite fractal dimension. This latter result is applied to show that the 2D Navier-Stokes equations on a non-cylindrical domain has a pullback attractor with finite fractal dimension. (AU)

Processo FAPESP: 21/01931-4 - Comportamento assintótico pullback para equações parabólicas não lineares com parte principal subdiferencial
Beneficiário:Heraclio Ledgar López Lázaro
Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 22/13001-4 - Dimensão fractal finita para equações parabólicas não-lineares com parte principal subdiferencial
Beneficiário:Heraclio Ledgar López Lázaro
Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado