Global smoothing for the periodic Benjamin equation in low-regularity spaces

Global smoothing for the periodic Benjamin equation in low-regularity spaces

This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most pol...

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Veröffentlicht in:Science China. Mathematics 2013-10, Vol.56 (10), p.2051-2061
Hauptverfasser: Shi, ShaoGuang, Li, JunFeng
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Sprache:eng
Schlagworte:
Applications of Mathematics
Astronomy
Benjamin方程
China
Evolution
Functions (mathematics)
KdV
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Polynomials
Smoothing
Symmetry
函数
周期性
多项式
对称性
德弗里斯
空间平滑
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description This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.
doi_str_mv 10.1007/s11425-013-4672-3
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source Springer Nature - Complete Springer Journals; Alma/SFX Local Collection
subjects Applications of Mathematics
Astronomy
Benjamin方程
China
Evolution
Functions (mathematics)
KdV
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Polynomials
Smoothing
Symmetry
函数
周期性
多项式
对称性
德弗里斯
空间平滑
title Global smoothing for the periodic Benjamin equation in low-regularity spaces
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