The $L^2$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state

Abstract

We study the non-scattering $L^2$ solution $u$ to the radial mass critical nonlinear Schrödinger equation with mass just above the ground state, and show that there exists a time sequence $\{t_n{\}}_n$, such that $u(t_n)$ weakly converges to the ground state $Q$ up to scaling and phase transformation. We also give some partial results on the mass concentration of the minimal mass blow up solution.

27 pages, all comments are welcome