The nonlinear Rayleigh‐Stokes problem with Riemann‐Liouville fractional derivative
Copyright policy )The nonlinear Rayleigh‐Stokes problem with Riemann‐Liouville fractional derivative
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.
- Xiangtan University China (People's Republic of)
- Macau University of Science and Technology Macao
Riemann-Liouville derivative, Fractional derivatives and integrals, Non-Newtonian fluids, existence, mild solution, Rayleigh-Stokes problem, Existence problems for PDEs: global existence, local existence, non-existence, Initial value problems for PDEs and systems of PDEs with constant coefficients, PDEs in connection with fluid mechanics, Fractional partial differential equations
Riemann-Liouville derivative, Fractional derivatives and integrals, Non-Newtonian fluids, existence, mild solution, Rayleigh-Stokes problem, Existence problems for PDEs: global existence, local existence, non-existence, Initial value problems for PDEs and systems of PDEs with constant coefficients, PDEs in connection with fluid mechanics, Fractional partial differential equations
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