Acta mathematica scientia, Series B >
LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL
Received date: 2010-10-27
Online published: 2012-05-20
Supported by
Supported by National Science Foundation of China (11071177) and Excellent Youth Foundation of Sichuan Province (2012JQ0011).
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear Schr¨odinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ ={u ∈ H1; ∫RN |x|2|u|2dx < +∞}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that |u(t, x)|2 → ||Q||2 L2 δx=x1 as t → T.
ZHU Shi-Hui , ZHANG Jian . LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1181 -1192 . DOI: 10.1016/S0252-9602(12)60090-3
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