Structure theorems for 2D linear and nonlinear Schrödinger equations

Abstract

This paper is devoted to the qualitative study of the nonlinear Schrödinger equation with exponential growth, where the Orlicz norm plays a crucial role. The approach we adopted in this paper which is based on profile decompositions consists of comparing the evolution of oscillations and concentration effects displayed by sequences of solutions to 2D linear and nonlinear Schrödinger equations associated to the same sequence of Cauchy data, up to small remainder terms both in Strichartz and Orlicz norms. The analysis we conducted in this work emphasizes the correlation between the nonlinear effect highlighted in the behavior of the solutions to the 2D nonlinear Schrödinger equation and the [Formula: see text]-oscillating component of the sequence of the Cauchy data.