Abstract
The purpose of this paper is to analyse the Rayleigh–Stokes problem for a heated generalized second-grade fluid with Riemann–Liouville fractional derivative. By virtue of the Galerkin method, the existence, uniqueness and regularity of weak solutions in \(L^{\infty }(0,b;L^2(\Omega ))\) \(\bigcap L^2(0,b;H_0^1(\Omega ))\) of the proposed problem are obtained. Furthermore, we prove an improved regularity result of weak solutions in the case of \(h\in H^2(\Omega )\) and \(f\in L^2(0,b;L^2(\Omega ))\).
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Project supported by National Natural Science Foundation of China (12070396).
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Wang, J.N., Zhou, Y., Alsaedi, A. et al. Well-posedness and regularity of fractional Rayleigh–Stokes problems. Z. Angew. Math. Phys. 73, 161 (2022). https://doi.org/10.1007/s00033-022-01808-7
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DOI: https://doi.org/10.1007/s00033-022-01808-7