LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

doi:10.1016/S0252-9602(12)60090-3

Abstract

Abstract:

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 δ_x_=x1 as t → T.

Key words: Nonlinear Schr¨odinger equation, Stark potential, blow-up solution, limiting behavior, mass concentration

CLC Number:

35Q55

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.

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