Rate of $L^2$-concentration of the blow-up solution
for critical nonlinear Schrödinger equation with potential
Jian Zhang - College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China (email)
Abstract: We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of Merle and Tsutsumi's arguments as well as Carles' transform, the $L^2$-concentration property of radially symmetric blow-up solutions is obtained.
Keywords: Nonlinear Schrödinger equation, repulsive harmonic potential, blow-up solution, $L^2$-concentration.
Received: October 2010; Revised: January 2011; Available Online: March 2011.
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