| 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,2017,38(3):243~256 |
| Davey-Stewartson系统粗糙爆破解的极限行为 |
| Limiting Behavior of Rough Blow-up Solutions to the Davey-Stewartson System |
| Received:September 17, 2015 Revised:September 21, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0019 |
| 中文关键词: Davey-Stewartson system, Rough blow-up solution, Limiting |
| 英文关键词:Davey-Stewartson system, Rough blow-up solution, Limiting |
| 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. |
|
| Hits: 819 |
| Download times: 604 |
| 中文摘要: |
| 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$H^s$ ($s<1$)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$H^{s}(\mathbb{R}^2)$
(其中 $s>s_0$, 且 $s_0\leq \frac{1+\sqrt{11}}{5}\approx 0.8633$)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. |
| 英文摘要: |
| 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
$s_0\leq \frac{1+\sqrt{11}}{5}\approx 0.8633$. |
| View Full Text View/Add Comment Download reader |
| Close |
