Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911698174083072 |
|---|---|
| author | Peng, Li Deng, Lin He, Jia Wei |
| author_facet | Peng, Li Deng, Lin He, Jia Wei |
| contents | In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second grade fluid. We first investigate the global well-posedness of solutions consisting of global Lipschitz condition by a weighted space $\mathcal C$. Utilizing the topology convergence on compact subsets of $\mathcal C$, we construct a semi-dynamical system that satisfies the semi-group structure. It also is shown that this semi-dynamical system has an attracting set when the vector field function satisfies a dissipativity condition and a local Lipschitz condition. With the asymptotic compactness, we also establish the existence of generalized attractors in $\mathcal C_α$ of subspace of $\mathcal C$ the weighted norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations Peng, Li Deng, Lin He, Jia Wei Dynamical Systems 35B41, 35R11 In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second grade fluid. We first investigate the global well-posedness of solutions consisting of global Lipschitz condition by a weighted space $\mathcal C$. Utilizing the topology convergence on compact subsets of $\mathcal C$, we construct a semi-dynamical system that satisfies the semi-group structure. It also is shown that this semi-dynamical system has an attracting set when the vector field function satisfies a dissipativity condition and a local Lipschitz condition. With the asymptotic compactness, we also establish the existence of generalized attractors in $\mathcal C_α$ of subspace of $\mathcal C$ the weighted norm. |
| title | Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations |
| topic | Dynamical Systems 35B41, 35R11 |
| url | https://arxiv.org/abs/2605.10421 |