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On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN
Advances in Nonlinear Analysis ( IF 4.2 ) Pub Date : 2022-01-01 , DOI: 10.1515/anona-2021-0211
Jia Wei He 1 , Yong Zhou 2, 3 , Li Peng 2 , Bashir Ahmad 3
Affiliation  

We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝ N , which is derived from a non-Newtonain fluid for a generalized second grade fluid with Riemann-Liouville fractional derivative. We show that a solution operator involving the Laplacian operator is very effective to discuss the proposed problem. In this paper, we are concerned with the global/local well-posedness of the problem, the approaches rely on the Gagliardo-Nirenberg inequalities, operator theory, standard fixed point technique and harmonic analysis methods. We also present several results on the continuation, a blow-up alternative with a blow-up rate and the integrability in Lebesgue spaces.

中文翻译:

关于ℝN上带分数导数的半线性Rayleigh-Stokes问题的适定性

我们致力于研究 ℝ N 上的半线性时间分数 Rayleigh-Stokes 问题,该问题源自具有 Riemann-Liouville 分数导数的广义二级流体的非牛顿流体。我们表明,涉及拉普拉斯算子的解算子对于讨论所提出的问题非常有效。在本文中,我们关注问题的全局/局部适定性,这些方法依赖于 Gagliardo-Nirenberg 不等式、算子理论、标准不动点技术和谐波分析方法。我们还提出了关于延续的几个结果,一个具有爆破率的爆破替代方案和 Lebesgue 空间的可积性。
更新日期:2022-01-01
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