Dynamics of threshold solutions for the energy-critical inhomogeneous NLS
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910585909673984 |
|---|---|
| author | Liu, Xuan Yang, Kai Zhang, Ting |
| author_facet | Liu, Xuan Yang, Kai Zhang, Ting |
| contents | In this article, we study the long-time dynamics of threshold solutions for the focusing energy-critical inhomogeneous Schrödinger equation and classify the corresponding threshold solutions in dimensions $d=3,4,5$. We first show the existence of special threshold solutions $W^\pm$ by constructing a sequence of approximate solutions in suitable Lorentz space, which exponentially approach the ground state $W$ in one of the time directions. We then prove that solutions with threshold energy either behave as in the subthreshold case or agree with $W, W^+$ or $W^-$ up to the symmetries of the equation. The proof relies on detailed spectral analysis of the linearized Schrödinger operator, the relevant modulation analysis, the global Virial analysis, and the concentration compactness argument in the Lorentz space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of threshold solutions for the energy-critical inhomogeneous NLS Liu, Xuan Yang, Kai Zhang, Ting Analysis of PDEs 35Q55 In this article, we study the long-time dynamics of threshold solutions for the focusing energy-critical inhomogeneous Schrödinger equation and classify the corresponding threshold solutions in dimensions $d=3,4,5$. We first show the existence of special threshold solutions $W^\pm$ by constructing a sequence of approximate solutions in suitable Lorentz space, which exponentially approach the ground state $W$ in one of the time directions. We then prove that solutions with threshold energy either behave as in the subthreshold case or agree with $W, W^+$ or $W^-$ up to the symmetries of the equation. The proof relies on detailed spectral analysis of the linearized Schrödinger operator, the relevant modulation analysis, the global Virial analysis, and the concentration compactness argument in the Lorentz space. |
| title | Dynamics of threshold solutions for the energy-critical inhomogeneous NLS |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2409.00073 |