Weak solutions of the Robin problem for the Oseen system

摘要

We study the Robin problem for the Oseen system in the Sobolev space W1,q(Ω?Rm)×Lq(Ω)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$W^{1,q}(varOmega ;{{mathbb {R}}}^m)times L^q(varOmega )$$end{document} on a bounded domain Ω?Rmdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$varOmega subset {{mathbb {R}}}^m$$end{document} with Lipschitz boundary for m=2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m=2$$end{document} or m=3documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$m=3$$end{document}. We prove the unique solvability of the problem for 3/2