Limiting behavior of blow-up solutions of the NLSE with a stark potential

Abstract

This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear Schrödinger 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||L22δx=x1 as t →T.