Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities  

作　　者：Zai Hui GAN Bo Ling GUO Chun Xiao GUO 

机构地区：[1]College of Mathematics and Software Science,Sichuan Normal University [2]Institute of Applied Physics and Computational Mathematics [3]Department of Mathematics,China University of Mining and Technology Beijing

出　　处：《Acta Mathematica Sinica,English Series》2012年第9期1917-1936,共20页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11171241, 10801102,11071177);Sichuan Youth Science and Technology Foundation (Grant No. 07ZQ026-009);China Postdoctoral Science Foundation Funded Project

摘　　要：This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.

关 键 词：Generalized Zakharov system blowing up combined power-type nonlinearities Lyapunov function in time 

分 类 号：O175[理学—数学]