On the concentration properties for the nonlinear Schrödinger equation with a Stark potential

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.