We study the non-scattering $L^{2}$ solution $u$ to the radial focusing mass-critical nonlinear Schrödinger equation with mass just above the ground state, and show that there exists a time sequence… Click to show full abstract
We study the non-scattering $L^{2}$ solution $u$ to the radial focusing 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 phenomena of the minimal mass blow-up solution.
               
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