分数阶Rayleigh-Stokes方程Besov-Morrey空间解的适定性结果

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2023-11-22 DOI:10.1007/s12346-023-00897-7

Li Peng, Yong Zhou

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引用次数: 0

摘要

本文证明了一类具有记忆的广义二级流体在非牛顿流体中导出的分数阶瑞利-斯托克斯方程的长时间存在性。更确切地说，我们讨论了Besov-Morrey空间中全局解的存在性、唯一性、对初值的连续依赖性和渐近行为。该证明基于实插值、可解算子和不动点参数。我们的结果被公式化，允许一个更大的类的初始值比以前的工作，该方法也适用于分数扩散情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.