English

Dynamic of threshold solutions for energy-critical NLS

Analysis of PDEs 2007-11-01 v1

Abstract

We consider the radial energy-critical non-linear focusing Schr\"odinger equation in dimension N=3,4,5. An explicit stationnary solution, W, of this equation is known. In a previous work by C. Carlos and F. Merle, the energy E(W) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present article, we study the dynamics at the critical level E(u)=E(W) and classify the corresponding solutions. This gives in particular a dynamical characterization of W.

Keywords

Cite

@article{arxiv.0710.5915,
  title  = {Dynamic of threshold solutions for energy-critical NLS},
  author = {Thomas Duyckaerts and Frank Merle},
  journal= {arXiv preprint arXiv:0710.5915},
  year   = {2007}
}

Comments

Preprint, to be published in GAFA

R2 v1 2026-06-21T09:38:28.058Z