Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities

Tuan, Pham Thanh; Ke, Tran Dinh; Thang, Nguyen Nhu

doi:10.1007/s13540-023-00133-8

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…By using an operator-theoretic approach, Bazhlekova et al [19] obtained the well-posedness and Sobolev regularity of the homogenous Rayleigh-Stokes problem and Bazhlekova [20] showed a well-posed result associated with the bounded C 0 a-semigroup by means of the subordination principle. Pham et al [21] studied a final-value problem involving weak-valued nonlinearities and obtained the existence and Hölder regularity by using the regularity of the resolvent operators. Tran and Nguyen [22] obtained the solvability and Hölder regularity on the embeddings of fractional Sobolev spaces.…”

Section: Introductionmentioning

confidence: 99%

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

2023

Fractal Fract

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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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Section: Introductionmentioning

confidence: 99%

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

2023

Fractal Fract

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Existence and regularity of solutions for semilinear fractional Rayleigh–Stokes equations

Jiang,

Ren,

Wei

2024

Z. Angew. Math. Phys.

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The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

Peng,

Zhou

2023

Qual. Theory Dyn. Syst.

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Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities

Cited by 3 publications

References 27 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

Existence and regularity of solutions for semilinear fractional Rayleigh–Stokes equations

The Well-Posedness Results of Solutions in Besov-Morrey Spaces for Fractional Rayleigh-Stokes Equations

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