BLOW-UP SOLUTIONS FOR NON-SCALE-INVARIANT NONLINEAR SCHRÖDINGER EQUATION IN ONE DIMENSION.

In this paper, we consider the mass-critical nonlinear Schrödinger equation in one dimension. Ogawa-Tsutsumi [Proc. Amer. Math. Soc. 111 (1991), no. 2, 487-496] proved a blow-up result for negative energy solution by using a scaling argument for initial data. In general, a equation with a linear potential does not have a scale invariant, so the method by Ogawa-Tsutsumi cannot be used directly to that. In this paper, we prove a blow-up result for the equation with the linear potential by modifying the argument of Ogawa-Tsutsumi. [ABSTRACT FROM AUTHOR]