| 孙旭阳,尹俊平,高真圣.带有幂型的广义Zakharov方程组解的爆破率的下界估计[J].数学年刊A辑,2013,34(1):63~80 |
| 带有幂型的广义Zakharov方程组解的爆破率的下界估计 |
| Lower-Bound Estimates for the Blow-up Rate of Solutions to the Generalized Zakharov Equations with a Power-Type Nonlinearity |
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| DOI： |
| 中文关键词: 广义Zakharov方程组,爆破率,下界估计,幂型非线性 |
| 英文关键词:Generalized Zakharov equations,Blow-up rate,Lower-bound estimate,Power-type nonlinearity |
| 基金项目:国家自然科学基金 (No.11101044),国务院侨务办自然科学基金(No.11QZR18) |
| Author Name | Affiliation | E-mail | | SUN Xuyang | Public Teaching Center, Heping Campus, Jilin University, Changchun 130061,
China. | 83529083@qq.com | | YIN Junping | Corresponding author. Institute of Applied Physics and Computational Mathematics,
Beijing 100088, China. | yinjp829829@126.com | | GAO Zhensheng | School of Mathematical Sciences, Huaqiao University, Quangzhou 362021, Fujian,
China. | gaozhensheng@hqu.edu.cn |
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| 中文摘要: |
| 主要研究了关于$\mathbb{R}^2$中一类带有幂型非线性的广义Zakharov方程组的Cauchy问题的有限时间爆破解的爆破率的下界估计. 在$\alpha\leq 0$ 和 $p\geq 3$条件下, 对于Cauchy问题任意给定的属于能量空间$H^{1}({\mathbb{R}}^{2})\timesL^{2}({\mathbb{R}}^{2})\times L^{2}({\mathbb{R}}^{2})$的有限时间的爆破解, 得到了对于$t$靠近有限爆破时间$T$时的爆破率的最优下界估计. 此外,给出了Cauchy问题维里等式的一个应用. |
| 英文摘要: |
| This paper is concerned with lower-bound estimates for the blow-up rate of a finite-time blow-up solution to the Cauchy problem for a class of generalized Zakharov equations with a power-type nonlinearity in $\mathbb{R}^2$. Under the conditions $\alpha\leq 0$ and $p\geq 3$, for a given finite-time blow-up solution to the Cauchy problem in the energy space $H^{1}({\mathbb{R}}^{2})\times L^{2}({\mathbb{R}}^{2})\times L^{2}({\mathbb{R}}^{2})$, the authors obtain optimal lower-bound estimates for the blow-up rate of the finite-time blow-up solution for $t$ near the finite blow-up time $T$. In addition, an application of the Virial identity of the Cauchy problem is given. |
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