| Davey-Stewartson系统粗糙爆破解的极限行为 |
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| 引用本文： | 杨晗,朱世辉.Davey-Stewartson系统粗糙爆破解的极限行为[J].数学年刊A辑(中文版),2017,38(3):243-256. |
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| 作者姓名： | 杨晗 朱世辉 |
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| 作者单位： | 西南交通大学数学学院, 成都 610031.,通讯作者. 四川师范大学数学与软件科学学院, 成都 610066. |
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| 基金项目： | 本文受到国家自然科学基金(No.11371267,No.11501395)和四川省杰出青年基金(No.2014JQ0039)的资助. |
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| 摘 要： | 研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.
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| 关 键 词： | Davey-Stewartson system Rough blow-up solution Limiting |
| 收稿时间： | 2015/9/17 0:00:00 |
| 修稿时间： | 2016/9/21 0:00:00 |
Limiting Behavior of Rough Blow-up Solutions to the Davey-Stewartson System |
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| YANG Han and ZHU Shihui.Limiting Behavior of Rough Blow-up Solutions to the Davey-Stewartson System[J].Chinese Annals of Mathematics,2017,38(3):243-256. |
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| Authors: | YANG Han and ZHU Shihui |
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| Institution: | School of Mathematics, Southwest Jiaotong University,Chengdu 610031, China. and Corresponding author. Department of Mathematics, Sichuan Normal University,Chengdu 610066, China. |
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| Abstract: | This paper deals with the dynamical properties of the rough
blow-up solutions, which are the solutions in the lower regular
space $H^s$ with $s <1$, to Davey-Stewartson system. In this case,
there is no conservation of energy. By using the $I$-method and
profile decomposition argument, we obtain the limiting profile,
non-existence of $L^2$ strong limit and $L^2$ concentration of the
rough blow-up solutions in $H^{s}(\mathbb{R}^2)$ with $s>s_0$, where
$s_0\leq \frac{1+\sqrt{11}}{5}\approx 0.8633$. |
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| Keywords: | Davey-Stewartson system Rough blow-up solution Limiting |
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