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

Well-posedness and blow-up results for a class of nonlinear fractional Rayleigh-Stokes problem. (English) Zbl 1503.35278

Adv. Nonlinear Anal. 11, 1579-1597 (2022).
Summary: 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 \(\varepsilon\)-regular mild solutions are obtained. Furthermore, a unique continuation result and a blow-up alternative result of \(\varepsilon\)-regular mild solutions are given in the end.

Cited in 5 Documents

MSC:

35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids

Keywords:

Riemann-Liouville fractional derivative; Rayleigh-Stokes problem; \(\varepsilon \)-regular mild solutions; well-posedness; blow-up
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