Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations
Abstract
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 π. Utilizing the topology convergence on compact subsets of π, 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 πΞ± of subspace of π the weighted norm.
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BibTeX
@misc{peng2026longtime,
title = {{Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations}},
author = {Li Peng and Lin Deng and Jia Wei He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.10421},
eprint = {2605.10421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10421},
}
RIS
TY - UNPB
TI - Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations
AU - Li Peng
AU - Lin Deng
AU - Jia Wei He
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2605.10421
UR - https://arxiv.org/abs/2605.10421
AB - 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 π. Utilizing the topology convergence on compact subsets of π, 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 π_Ξ± of subspace of π the weighted norm.
ER -