Remarks on the Blowup for the $L^2$‐Critical Nonlinear Schrödinger Equations

Source abstract

This paper is dedicated to the formation of singularities of the solutions of $L^2$‐critical nonlinear Schrödinger equations. We prove a refined compactness lemma adapted to the blowup analysis, and we use it to improve the recent result by Colliander et al. [Math. Res. Lett., 12 (2005), pp. 357–375] on the concentration in the $L^2$‐critical nonlinear Schrödinger equation below $H^1$.