Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

Frank Merle, Pierre Raphael, Jeremie Szeftel

We consider the focusing nonlinear Schrödinger equations $i{\partial }_{t}u+\Delta u+u|u{|}^{p-1}=0$ in dimension $1\le N\le 5$ and for slightly $L^2$ supercritical nonlinearities $p_c<p<(1…