Blow up and near soliton dynamics for the $L^2$ critical gKdV equation
Blow up and near soliton dynamics for the $L^2$ critical gKdV equation
复制标题
$L^2$ 临界 gKdV 方程的爆炸和近孤子动力学
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Raphaël
中科院分区：
文献类型：
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作者：
Y. Martel;F. Merle;P. Raphaël
这些注记给出了文[22，23，24]中关于质量临界（gKdV）方程ut +（uxx + u）x = 0的主要结果。这些工作重新审视了几个方向的孤子族附近的爆破现象：稳定爆破的定义和分类的所有可能的行为在一个合适的功能设置，描述的最小质量爆破在H，建设各种异国情调的爆破率在H中，包括在无限时间的增长。
These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation ut + (uxx + u)x = 0 for initial data in H close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in H, construction of various exotic blow up rates in H, including grow up in infinite time.