Impulsive non‐autonomous dynamical systems and impulsive cocycle attractors |
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| Authors: | Everaldo M Bonotto Matheus C Bortolan Tomás Caraballo Rodolfo Collegari |
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| Institution: | 1. Instituto de Ciências Matemáticas e de Computa??o, Universidade de S?o Paulo, Campus de S?o Carlos, S?o Carlos, SP, Brazil;2. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, Brazil;3. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Sevilla, Spain |
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| Abstract: | In this work, we define the notions of ‘impulsive non‐autonomous dynamical systems’ and ‘impulsive cocycle attractors’. Such notions generalize (we will see that not in the most direct way) the notions of autonomous dynamical systems and impulsive global attractors in the current published literature. We also establish conditions to ensure the existence of an impulsive cocycle attractor for a given impulsive non‐autonomous dynamical system, which are analogous to the continuous case. Moreover, we prove the existence of such attractor for a non‐autonomous 2D Navier–Stokes equation with impulses, using energy estimates. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | non‐autonomous dynamical systems cocycle attractors impulses Navier– Stokes equation |
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