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 α ≥ 0 and $1 + \tfrac{4} {N} \leqslant p < \tfrac{{N + 2}} {{N - 2}}$ or α < 0 and $1 < p < 1 + \tfrac{4} {N}$ (N = 2, 3); the other is established under the condition N = 3, $1 < p < \tfrac{{N + 2}} {{N - 2}}$ 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.