By Dr. Fernando Cortez. Escuela Politécnica Nacional del Ecuador
Seminar Date: 2022-08-25
In this talk, we consider the damped Navier-Stokes-Bardina model posed on the whole threedimensional. These equations arise from some oceanic model and, from the mathematical point of view, they write down as the well-know Navier-Stokes equations with an additional nonlocal operator in their nonlinear transport term, and moreover, with an additional damping term depending of a parameter. We study first the existence and uniqueness of global in time weak solutions in the energy space. Thereafter, we are interested in describing their long time behavior. For this, we use some tools in the theory of dynamical systems to prove the existence of a global attractor, which is compact subset in the energy space attracting all the weak solutions when the time goes to infinity. Moreover, we derive an upper bound for the fractal dimension of the global attractor associated to these equations.