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

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.