On the concentration properties for the nonlinear Schrödinger equation with a Stark potential |
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| Authors: | Zhu Shihui Zhang Jian |
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| Institution: | aVisual Computing and Virtual Reality Key Laboratory, Sichuan Normal University, Chengdu 610066, China;bCollege of Mathematics, Sichuan University, Chengdu 610064, China |
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| Abstract: | In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrödinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrödinger 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. |
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| Keywords: | nonlinear Schrö odinger equation blow-up solution blow-up point L2-concentration concentration compact principle |
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