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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-11-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2021-0211 |
| _version_ | 1817997610074505216 |
|---|---|
| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-14T02:39:44Z |
| format | Article |
| id | doaj.art-1ea552bb77eb4029a5f6a38066d57d22 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-04-14T02:39:44Z |
| publishDate | 2021-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-1ea552bb77eb4029a5f6a38066d57d222022-12-22T02:17:09ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-11-0111158059710.1515/anona-2021-0211On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝNHe Jia Wei0Zhou Yong1Peng Li2Ahmad Bashir3College of Mathematics and Information Science, Guangxi University, Nanning, 530004, ChinaFaculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, ChinaFaculty of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, ChinaNonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi ArabiaWe 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.https://doi.org/10.1515/anona-2021-0211fractional derivativerayleigh-stokes problemwell-posednessintegrability26a3334a1235r11 |
| spellingShingle | He Jia Wei Zhou Yong Peng Li Ahmad Bashir On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝN Advances in Nonlinear Analysis fractional derivative rayleigh-stokes problem well-posedness integrability 26a33 34a12 35r11 |
| title | 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_short | 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 |
| topic | fractional derivative rayleigh-stokes problem well-posedness integrability 26a33 34a12 35r11 |
| url | https://doi.org/10.1515/anona-2021-0211 |
| work_keys_str_mv | AT hejiawei onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT zhouyong onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT pengli onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn AT ahmadbashir onwellposednessofsemilinearrayleighstokesproblemwithfractionalderivativeonrn |