Soliton resolution for the energy critical damped wave equations in the radial case
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909134520057856 |
|---|---|
| author | Gu, Jingyuan Zhao, Lifeng |
| author_facet | Gu, Jingyuan Zhao, Lifeng |
| contents | We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-Δu+α\partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial radial stationary solution $W$, called the ground state, which is unique up to sign and scale. We prove that any bounded energy norm solution behaves asymptotically as a superposition of the modulated ground states and a radiation term. In the global case, particularly, the solution converges to a pure multi-bubble due to the damping effect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04115 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Soliton resolution for the energy critical damped wave equations in the radial case Gu, Jingyuan Zhao, Lifeng Analysis of PDEs We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-Δu+α\partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial radial stationary solution $W$, called the ground state, which is unique up to sign and scale. We prove that any bounded energy norm solution behaves asymptotically as a superposition of the modulated ground states and a radiation term. In the global case, particularly, the solution converges to a pure multi-bubble due to the damping effect. |
| title | Soliton resolution for the energy critical damped wave equations in the radial case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.04115 |