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Palestrante: Pedro Marín-Rubio

Responsável: Estefani Moraes Moreira (Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.)

Modo: À distância

Salvar atividade no Google Calendar Webinar on Evolution Equations and Dynamical Systems

Resumo: The 3d Navier-Stokes-Voigt model was proposed by Cao, Lunasin and Titi (cf. [Cao, Lunasin, Titi, Commun. Math. Sci. 2006]) as a regularization of the 3d-Navier-Stokes equations for the purpose of direct numerical simulations. It is a non classical diffusion equation, which allows well-posedness but no immediate smoothing of the solution. Indeed the semigroup behaves asymptotically compact, as damped hyperbolic systems. Long-time behavior has been analyzed by many authors in several situations. We survey some old results (cf. [J. García-Luengo, PMR, J. Real, Nonlinearity 2012]) in the case of a non-autonomous variation of the problem (but without delay) and, if possible, some recent results in the case of delay terms included (cf. [J. García-Luengo, PMR, EJQTDE 2024]). Existence and regularity of pullback attractors will be discussed.

This work has been done in collaboration with Julia García-Luengo (Universidad Politécnica de Madrid).

J. García-Luengo, P. Marín-Rubio, J. Real, Pullback attractors for three-dimensional non-autonomous Navier-Stokes-Voigt equations, Nonlinearity 25 (2012), 1-26.

J. García-Luengo, P. Marín-Rubio, Existence and regularity of pullback attractors for a 3D non-autonomous Navier-Stokes-Voigt model with finite delay, Electronic Journal of Qualitative Theory of Differential Equations, 14 (2024), 1-35.
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