Blow up of the critical norm for some radial L^2 super critical nonlinear Schrodinger equations

Frank Merle, Pierre Raphael

We consider the nonlinear Schrödinger equation $i{u}_t=-\Delta u-|u{|}^{p-1}u$ in dimension $N\ge 3$ in the $L^2$ super critical range $1+\frac{4}{N}<p<\frac{N+2}{N-2}$. The corresponding s…