On Global Solvability and Regularity for Generalized Rayleigh–Stokes Equations with History-Dependent Nonlinearities

Ke, Tran Dinh; Thang, Nguyen Nhu

doi:10.1007/s00009-023-02318-0

Mediterr. J. Math.

2023

DOI: 10.1007/s00009-023-02318-0

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On Global Solvability and Regularity for Generalized Rayleigh–Stokes Equations with History-Dependent Nonlinearities

Tran Dinh Ke

Nguyen Nhu Thang

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The Hölder Regularity for Abstract Fractional Differential Equation with Applications to Rayleigh–Stokes Problems

2023

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In this paper, we studied the Hölder regularities of solutions to an abstract fractional differential equation, which is regarded as an abstract version of fractional Rayleigh–Stokes problems, rising up to describing a non-Newtonian fluid with a Riemann–Liouville fractional derivative. The purpose of this article was to establish the Hölder regularities of mild solutions, classical solutions, and strict solutions. We introduced an interpolation space in terms of an analytic resolvent to lower the spatial regularity of initial value data. By virtue of the properties of analytic resolvent and the interpolation space, the Hölder regularities were obtained. As applications, the main conclusions were applied to the regularities of fractional Rayleigh–Stokes problems.

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The Hölder Regularity for Abstract Fractional Differential Equation with Applications to Rayleigh–Stokes Problems

2023

Fractal Fract

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On Global Solvability and Regularity for Generalized Rayleigh–Stokes Equations with History-Dependent Nonlinearities

Cited by 1 publication

References 22 publications

The Hölder Regularity for Abstract Fractional Differential Equation with Applications to Rayleigh–Stokes Problems

The Hölder Regularity for Abstract Fractional Differential Equation with Applications to Rayleigh–Stokes Problems

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