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 Schr\"odinger equation [ i\partial_t u + \Delta u + |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 $N\ge1$.