| Full text | |
| Author(s): |
Cui, Hongyong
;
Lopez, Rodiak Nicolai Figueroa
;
Lopez-Lazaro, Heraclio Ledgar
;
Simsen, Jacson
Total Authors: 4
|
| Document type: | Journal article |
| Source: | MATHEMATISCHE ANNALEN; v. 390, n. 4, p. 56-pg., 2024-06-14. |
| Abstract | |
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) | |
| FAPESP's process: | 21/01931-4 - Pullback attractor for non-linear parabolic equations with subdifferential principal part |
| Grantee: | Heraclio Ledgar López Lázaro |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 22/13001-4 - Finite fractal dimension for non-linear parabolic equations with subdifferential principal part |
| Grantee: | Heraclio Ledgar López Lázaro |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |