We consider the focusing mass-critical nonlinear Schr\"odinger equation and prove that blowup solutions to this equation with initial data in $H^s(\R^d)$, $s > s_0(d)$ and $d\geq 3$, concentrate at least the mass of the ground state at the blowup time. This extends recent work by J. Colliander, S. Raynor, C. Sulem, and J. D. Wright, \cite{ crsw}, T. Hmidi and S. Keraani, \cite{ hk}, and N. Tzirakis, \cite{ tzirakis}, on the blowup of the two-dimensional and one-dimensional mass-critical focusing NLS below the energy space to all dimensions $d\ge 3$.
Categories: math.AP