Blowing up of solutions to the Cauchy problem for the generalized Zakharov system with combined power-type nonlinearities

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• 作者：Zai Hui Gan (1) ganzaihui2008cn@yahoo.com.cn
  Bo Ling Guo (2) gbl@iapcm.ac.cn
  Chun Xiao Guo (3) guochunxiao1983@sina.com
• 关键词：Generalized Zakharov system &#8211 ; blowing up &#8211 ; combined power ; type nonlinearities &#8211 ; Lyapunov function in time
• 刊名：Acta Mathematica Sinica
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：28
• 期：9
• 页码：1917-1936
• 全文大小：285.0 KB
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• 作者单位：1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610068 P. R. China2. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088 P. R. China3. Department of Mathematics, China University of Mining and Technology Beijing, Beijing, 100083 P. R. China
• ISSN：1439-7617

文摘

This paper deals with blowing up of solutions to the Cauchy problem for a class of generalized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for c ₀ = +∞ we obtain two finite time blow-up results of solutions to the aforementioned system. One is obtained under the condition α ≥ 0 and $1 + \tfrac{4} {N} \leqslant p 1 + \tfrac{4} {N} \leqslant p or α < 0 and $1 1 (N = 2, 3); the other is established under the condition N = 3, $1 1 and α(p − 3) ≥ 0. On the other hand, for c ₀ < +∞ and α(p − 3) ≥ 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.