The global well‐posedness for nonlinear Schrödinger equation with the delta potential in the energy space

Abstract

In this paper, we concern with the global well‐posedness for nonlinear Schrödinger equation with a Dirac delta potential ( ‐NLS): Firstly, we give a new variational characterization of the solitary waves of ( ‐NLS) by making use of the symmetric decreasing rearrangement and constrained minimization argument. Secondly, we construct an invariant set , via the variational characterization of the solitary waves. Finally, we show the solutions, with initial data in , exist globally.