The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2000-08

AUTHORS

Masao Yamazaki

ABSTRACT

Abstract. We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time with initial data, with domain either the whole space, the half space or an exterior domain of dimension \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $n \ge 3$\end{document}. We give conditions on the external force sufficient for the unique existence of small solutions in the weak-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $L^n$\end{document} space bounded for all time. In particular, this result gives sufficient conditions for the unique existence and the stability of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $L^n$\end{document} space with time-independent external force. More... »

PAGES

635-675

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00004418

DOI

http://dx.doi.org/10.1007/pl00004418

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