Instability of singular equilibria of a wave kinetic equation
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911910576783360 |
|---|---|
| author | Escobedo, Miguel Menegaki, Angeliki |
| author_facet | Escobedo, Miguel Menegaki, Angeliki |
| contents | We consider the singular Rayleigh-Jeans equilibrium of the $4$-waves kinetic turbulence equation for the three dimensional Schrödinger equation. We first show the formation in finite time of a Dirac measure at zero frequency in the solution of the wave kinetic equation when the initial data has the form of Rayleigh-Jeans, truncated at large values of the energy. The initial value problem for the linearization around the singular Rayleigh-Jeans equilibria is then solved in several functional spaces. Then, long time convergence to a Dirac measure at the origin is described in detail for some of the solutions. This determines a basin of attraction of the Dirac measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instability of singular equilibria of a wave kinetic equation Escobedo, Miguel Menegaki, Angeliki Analysis of PDEs Mathematical Physics We consider the singular Rayleigh-Jeans equilibrium of the $4$-waves kinetic turbulence equation for the three dimensional Schrödinger equation. We first show the formation in finite time of a Dirac measure at zero frequency in the solution of the wave kinetic equation when the initial data has the form of Rayleigh-Jeans, truncated at large values of the energy. The initial value problem for the linearization around the singular Rayleigh-Jeans equilibria is then solved in several functional spaces. Then, long time convergence to a Dirac measure at the origin is described in detail for some of the solutions. This determines a basin of attraction of the Dirac measure. |
| title | Instability of singular equilibria of a wave kinetic equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2406.05280 |