| Full text | |
| Author(s): |
Yang, Xin-Guang
;
Qin, Yuming
;
Lu, Yongjin
;
Ma, To Fu
Total Authors: 4
|
| Document type: | Journal article |
| Source: | APPLIED MATHEMATICS AND OPTIMIZATION; v. 83, n. 3, p. 55-pg., 2019-11-06. |
| Abstract | |
This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier-Stokes equations with a non-homogeneous boundary condition on Lipschitz-like domains. With the presence of a time-dependent external force f(t) which only needs to be pullback translation bounded, we establish the existence of a minimal pullback attractor with respect to a universe of tempered sets for the corresponding non-autonomous dynamical system. We then give estimates on the finite fractal dimension of the attractor based on trace formula. Under the additional assumption that the external force is perturbed from a stationary force by a time-dependent perturbation, we also prove the upper semi-continuity of the attractors as the non-autonomous perturbation vanishes. Lastly, we investigate the regularity of these attractors when smoother initial data are given. Our results are new even for smooth domains. (AU) | |
| FAPESP's process: | 14/17080-0 - Nonautonomous dynamical systems of evolution equations on domains with moving boundary |
| Grantee: | Xinguang Yang |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |