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 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 . . 0 and 1+4N.p<N+2N.2 or . < 0 and 1<p<1+4N (N = 2, 3); the other is established under the condition N = 3, 1<p<N+2N.2 and .(p . 3) . 0. On the other hand, for c 0 < +. and .(p . 3) . 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.