On the blowup for the $L^2$-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class

Details On the blowup for the $L^2$-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class On the blowup for the $L^2$-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class

2006-06-28

arxiv.org/abs/math/0606737v2

Mathematics

Analysis of PDEs

Scientific paper

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 $d\ge 3$.

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