Well-posedness and regularity of fractional Rayleigh–Stokes problems

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∞(0,b;L2(Ω))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{\infty }(0,b;L^2(\Omega ))$$\end{document}⋂L2(0,b;H01(Ω))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bigcap L^2(0,b;H_0^1(\Omega ))$$\end{document} of the proposed problem are obtained. Furthermore, we prove an improved regularity result of weak solutions in the case of h∈H2(Ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h\in H^2(\Omega )$$\end{document} and f∈L2(0,b;L2(Ω))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\in L^2(0,b;L^2(\Omega ))$$\end{document}.