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Decay of solutions to the initial boundary value problem of the stokes system in the halfspace

机译:Decay of solutions to the initial boundary value problem of the stokes system in the halfspace

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Abstract The initial boundary problem of the Stokes system in the 3D halfspace is considered. The boundary condition subject on x3=0documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ x_3=0 $$end{document} is that the stress vanishes. Under the condition that the initial value is in L2∩L1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^2 cap L^1$$end{document} we derive the rate of decay in time of L2documentclass[12pt]{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 of solutions to this problem.
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