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arXiv · 2605.10421

Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations

Li Peng·Lin Deng·Jia Wei He
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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 $\mathcal C$. 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 $\mathcal C_\alpha$ of subspace of $\mathcal C$ the weighted norm.

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Li Peng, Lin Deng, Jia Wei He. 2026-05-11. Long-time dynamics for time-nonlocal generalized Rayleigh-Stokes equations. https://arxiv.org/abs/2605.10421

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