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 = +o...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.展开更多
We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimens...We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimension at most m-3.展开更多
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
文摘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.
文摘We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimension at most m-3.