Mass concentration phenomenon for the quintic nonlinear Schrödinger equation in one dimension

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.