On the stability of collapse in the critical case

Collapsing solutions in the Cauchy problem of the nonlinear Schrödinger equation i ∂ t ψ + ∇2ψ +‖ ψ‖ p ψ = 0 (x∈R d ) are considered in the so‐called critical case pd=4, where d is the spatial dimension. A stability theorem for radial collapse is presented which proves that the formation of the singularity remains ‘‘close’’ to the self‐similar collapsing solution with a spatial profile given by the ground state solitary wave, provided the energy H{ψ}