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 c0 = +∞ we obtain two finite time blow-up results of solutions to the aforementioned system. One is obtained under the condition α≥ 0 and 1 + 4/N ≤ p < N +2/N-2 or α < 0 and 1 < p < 1 + 4/N (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 c0 < +∞ and α(p-3) ≥ 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.