Classification of minimal mass blow-up solutions for an $L^2$ critical inhomogeneous NLS

Abstract

We establish the classification of minimal mass blow-up solutions of the $L^2$ critical inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^{\frac{4-2b}{N}}u = 0, \] thereby extending the celebrated result of Merle from the classic case $b=0$ to the case $0<b<\min \{2,N\}$, in any dimension $N\ge 1$.

15 pages