Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem

Jing Na Wang; Ahmed Alsaedi; Bashir Ahmad; Yong Zhou

doi:10.1515/anona-2022-0249

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$Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem$

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Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem

Jing Na Wang, Ahmed Alsaedi, Bashir Ahmad and Yong Zhou

Advances in nonlinear analysis, Vol.11(1), pp.1579-1597

12/06/2022

DOI: https://doi.org/10.1515/anona-2022-0249

Abstract

26A33

35E15

35R11

35R44

76D03

blow-up

Rayleigh-Stokes problem

Riemann-Liouville fractional derivative

well-posedness

ε-regular mild solutions

In this article, we consider the fractional Rayleigh-Stokes problem with the nonlinearity term satisfies certain critical conditions. The local existence, uniqueness and continuous dependence upon the initial data of -regular mild solutions are obtained. Furthermore, a unique continuation result and a blow-up alternative result of -regular mild solutions are given in the end.

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Title: Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem
Creators - without role: Jing Na Wang - Xiangtan University
Ahmed Alsaedi - King Abdulaziz University
Bashir Ahmad - King Abdulaziz University
Yong Zhou - King Abdulaziz University
Publication Details: Advances in nonlinear analysis, Vol.11(1), pp.1579-1597
Publisher: De Gruyter
Number of pages: 19
Identifiers: 9939699808331
Academic Unit: King Abdulaziz University
Language: English
Resource Type: Journal article