Pullback exponential attractor of dynamical systems associated with non-cylindrical problems

Huaccha Neyra J.; López-Lázaro H.; Rubio O.; Takaessu Junior C.R. · Journal of Mathematical Analysis and Applications (2025) · DOI: 10.1016/j.jmaa.2025.129332

Resumen

In this work, we present a way of approaching the theory of pullback exponential attractors for dynamical systems on time-dependent phase spaces (or dynamical systems associated with non-cylindrical problems). We will show that these types of dynamical systems satisfying the smoothing property have a pullback exponential attractor, extending the results for dynamical systems defined on a fixed phase space, e.g. [5,15,25]. Furthermore, we will apply this theory to show that the dynamical system associated with the 2D-Navier-Stokes equations on some non-cylindrical domain has a pullback exponential attractor on a suitable tempered universe that depends on the time integrability of the external force and the behavior of the initial conditions.

Instituciones: Universidad Nacional de Trujillo