On the Blowup for the $L^2$‐Critical Focusing Nonlinear Schrödinger Equation in Higher Dimensions below the Energy Class

Monica Visan, Xiaoyi Zhang
2007 SIAM Journal on Mathematical Analysis  
We consider the focusing mass-critical nonlinear Schrödinger equation and prove that blowup solutions to this equation with initial data in H s (R d ), s > s 0 (d) and d ≥ 3, concentrate at least the mass of the ground state at the blowup time. This extends recent work by Colliander et al. [Math. the blowup of the two-dimensional and one-dimensional mass-critical focusing nonlinear Schrödinger equation below the energy space to all dimensions d ≥ 3.
doi:10.1137/060663969 fatcat:3bcuwwinkrcwfh4l6h37gviqgi