The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations
The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations
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DOI：
10.1007/s12346-023-00897-7
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发表时间：
2023-11
影响因子：
1.4
通讯作者：
Li Peng;Yong Zhou
中科院分区：
文献类型：
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作者：
Li Peng;Yong Zhou
本文证明了非牛顿流体的分数阶Rayleigh-Stokes方程在广义二阶记忆流体中的一个长时间存在性结果。更精确地说，我们讨论了Besov-Morrey空间整体解的存在性、唯一性、对初值的连续依赖性和渐近性。证明是基于真实的插值，预解算子和不动点参数。我们的结果制定，允许一个更大的类的初始值比以前的作品，该方法也适用于分数扩散的情况。
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.