Local well-posedness for periodic Benjamin equation with small initial data

被引：0
作者：
Shaoguang Shi
Junfeng Li
机构：
[1] Linyi University,Department of Mathematics
[2] Ministry of Education,Laboratory of Mathematics and Complex Systems
[3] Beijing Normal University,School of Mathematical Sciences
来源：
Boundary Value Problems | / 2015卷
关键词：
Benjamin equation; local well-posedness; bilinear estimate; 35Q53; 35Q55;
D O I：
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摘要：
The local well-posedness of the periodic Benjamin equation with small initial value in Hs(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H^{s}(\mathbb{T})$\end{document}, s≥−1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$s\geq-{1}/{2}$\end{document}, is given. It is here shown that −1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$-{1}/{2}$\end{document} is the lower endpoint to obtain the bilinear estimates which are the crucial steps to obtain the local well-posedness by the Picard iteration.
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