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The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

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Abstract

In this paper, we prove a long time existence result for fractional Rayleigh-Stokes equations derived from a non-Newtonain fluid for a generalized second grade fluid with memory. More precisely, we discuss the existence, uniqueness, continuous dependence on initial value and asymptotic behavior of global solutions in Besov-Morrey spaces. The proof is based on real interpolation, resolvent operators and fixed point arguments. Our results are formulated that allows for a larger class in initial value than the previous works and the approach is also suitable for fractional diffusion cases.

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Funding

This work was supported by National Natural Science Foundation of China (12001462,12071396).

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Authors and Affiliations

  1. Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Li Peng

  2. School of Computer Science and Engineering, Macau University of Science and Technology, Macau, 999078, People’s Republic of China

    Yong Zhou

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  1. Li Peng
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  2. Yong Zhou
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L. Peng wrote the main manuscript text after discussing main technique with Y. Zhou. All authors reviewed the manuscript.

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Correspondence to Yong Zhou.

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Peng, L., Zhou, Y. The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations. Qual. Theory Dyn. Syst. 23, 43 (2024). https://doi.org/10.1007/s12346-023-00897-7

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