On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN
We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝN, 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 effectiv...
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De Gruyter
2021
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oai:doaj.org-article:1ea552bb77eb4029a5f6a38066d57d222021-12-05T14:10:40ZOn well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN2191-94962191-950X10.1515/anona-2021-0211https://doaj.org/article/1ea552bb77eb4029a5f6a38066d57d222021-11-01T00:00:00Zhttps://doi.org/10.1515/anona-2021-0211https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XWe are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝN, 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.He Jia WeiZhou YongPeng LiAhmad BashirDe Gruyterarticlefractional derivativerayleigh-stokes problemwell-posednessintegrability26a3334a1235r11AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 580-597 (2021) |
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DOAJ |
| collection |
DOAJ |
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EN |
| topic |
fractional derivative rayleigh-stokes problem well-posedness integrability 26a33 34a12 35r11 Analysis QA299.6-433 |
| spellingShingle |
fractional derivative rayleigh-stokes problem well-posedness integrability 26a33 34a12 35r11 Analysis QA299.6-433 He Jia Wei Zhou Yong Peng Li Ahmad Bashir On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| description |
We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝN, 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. |
| format |
article |
| author |
He Jia Wei Zhou Yong Peng Li Ahmad Bashir |
| author_facet |
He Jia Wei Zhou Yong Peng Li Ahmad Bashir |
| author_sort |
He Jia Wei |
| title |
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| title_short |
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| title_full |
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| title_fullStr |
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| title_full_unstemmed |
On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN |
| title_sort |
on well-posedness of semilinear rayleigh-stokes problem with fractional derivative on ℝn |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/1ea552bb77eb4029a5f6a38066d57d22 |
| work_keys_str_mv |
AT hejiawei onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT zhouyong onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT pengli onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT ahmadbashir onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn |
| _version_ |
1718371827492847616 |