We consider the L 2-critical quintic focusing nonlinear Schrödinger equation (NLS) on R. It is well known that H 1 solutions of the aforementioned equation blow up in finite time. In higher dimensions, for H 1 spherically symmetric blow-up solutions of the L 2-critical focusing NLS, there is a minimal amount of concentration of the L 2-norm (the mass of the ground state) at the origin. In this paper we prove the existence of a similar phenomenon for the one-dimensional case and rougher initial data, (u 0 ∈ H s, s < 1), without any additional assumption.
- Mass concentration
- Nonlinear Schrödinger equation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics