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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| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/1ea552bb77eb4029a5f6a38066d57d22 |
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| Sumario: | 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. |
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