A compactness result for inhomogeneous nonlinear Schrödinger equations. (February 2022) - Dinh, Van Duong; Keraani, Sahbi
Abstract: We establish a compactness property of the difference between nonlinear and linear operators (or the Duhamel operator) related to the inhomogeneous nonlinear Schrödinger equation. The proof is based on a refined profile decomposition for the equation. More precisely, we prove that any sequence ( ϕ n ) n of H 1 -functions which converges weakly in H 1 to a function ϕ, the corresponding solutions with initial data ϕ n can be decomposed (up to a remainder term) as a sum of the corresponding solution with initial data ϕ and solutions to the linear equation.