Standing ring blowup solutions for cubic nonlinear Schrödinger equations

Abstract

For all dimensions $N\ge 3$ we prove there exist solutions to the focusing cubic nonlinear Schrödinger equations that blow up on a set of codimension two. The blowup set is identified both as the site of $L^2$ concentration and by a bounded supercritical norm outside any neighborhood of the set. In all cases, the global $H^1$ norm grows at the log-log rate.