Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in 1d

We consider the L-critical quintic focusing nonlinear Schrödinger equation (NLS) on R. It is well known that H solutions of the aforementioned equation blow-up in finite time. In higher dimensions, for H spherically symmetric blow-up solutions of the L-critical focusing NLS, there is a minimal amount of concentration of the L-norm (the mass of the ground state) at the origin. In this paper we prove the existence of a similar phenomenon for the 1d case and rougher initial data, (u0 ∈ H , s < 1), without any additional assumption.