期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 44, 期 3, 页码 2431-2438出版社
WILEY
DOI: 10.1002/mma.5926
关键词
existence; mild solution; Rayleigh-Stokes problem; Riemann-Liouville derivative
资金
- Hunan Provincial Innovation Foundation for Postgraduate [XDCX2019B054]
- Fundo para o Desenvolvimento das Ciencias e da Tecnologia (FDCT) [0074/2019/A2]
- National Natural Science Foundation of China [11671339]
The paper investigates the existence of solutions for the nonlinear Rayleigh-Stokes problem for a generalized second grade fluid with Riemann-Liouville fractional derivative. It demonstrates that the solution operator of the problem is compact and continuous in the uniform operator topology, and provides an existence result of mild solutions for the nonlinear problem.
The Rayleigh-Stokes problem has gained much attention with the further study of non-Newtonain fluids. In this paper, we are interested in discussing the existence of solutions for nonlinear Rayleigh-Stokes problem for a generalized second grade fluid with Riemann-Liouville fractional derivative. We firstly show that the solution operator of the problem is compact and continuous in the uniform operator topology. Furtherly, we give an existence result of mild solutions for the nonlinear problem.
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