ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL

doi:10.1016/S0252-9602(11)60371-8

Abstract

Abstract:

In this paper, we study blow-up solutions of the Cauchy problem to the L² critical nonlinear Schr¨odinger equation with a Stark potential. Using the variational char-acterization of the ground state for nonlinear Schr¨odinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L²-concentration and rate of L²-concentration of blow-up solutions.

Key words: nonlinear Schr¨odinger equation, blow-up solution, blow-up point, L²-concentration, concentration compact principle

CLC Number:

35F25

ZHU Shi-Hui, ZHANG Jian. ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL[J].Acta mathematica scientia,Series B, 2011, 31(5): 1923-1938.

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