GLOBAL EXISTENCE OF THE SOLUTION OF NONLINEAR SCHRDINGER EQUATIONS IN EXTERIOR DOMAINS |
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引用本文: | 陈韵梅.GLOBAL EXISTENCE OF THE SOLUTION OF NONLINEAR SCHRDINGER EQUATIONS IN EXTERIOR DOMAINS[J].应用数学学报(英文版),1985,2(3):191-212. |
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作者姓名: | 陈韵梅 |
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作者单位: | Tongji University |
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摘 要: | In this paper,we discuss the problem for the nonlinear Schr(?)dinger equation(?)where Ω is the exterior domain of a compact set in B~n,a_j(u)=O(|u|),b_j(u)=O(|u|)(1≤j≤n),c(u)=O(|u|~2)near u=0.If n≥5,some Sobolev norm of u_0(x)is sufficiently small,under suitableassumptions on smoothnessand and compatibility and the shape of Ω,we get that the problem has aunique global solution u(t,x),with the decay estimate‖u(t,·)‖_(L(?)(Ω))=O(t~(-n/4)),‖u(t,·)‖_(L~4(Ω))=O(t~(-n/4)),t→+∞.
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