Abstract A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the L2documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^2$$end{document} norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the Lβ+1documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^{beta +1}$$end{document} norm for the perturbation temperature, where β>1documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$beta >1$$end{document}.
展开▼
