Damping-Diffusion-Noise Interactions in the Stochastic Camassa--Holm Equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912067313729536 |
|---|---|
| author | Alonso-Orán, Diego Pang, Peter H. C. Tang, Hao |
| author_facet | Alonso-Orán, Diego Pang, Peter H. C. Tang, Hao |
| contents | We investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa--Holm equations that incorporate these additional factors. Initially, a local-in-time theory is developed, covering the existence, uniqueness, and a blow-up criterion under relatively general conditions for these interacting factors. Subsequently, we identify different conditions on the interactions between damping, diffusion, and noise that enable the global regularity and long-time behaviour of classical solutions. Notably, we demonstrate the existence of an evolution system of measures, generalising the concept of invariant measures to the time-inhomogeneous system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07649 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Damping-Diffusion-Noise Interactions in the Stochastic Camassa--Holm Equation Alonso-Orán, Diego Pang, Peter H. C. Tang, Hao Analysis of PDEs We investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa--Holm equations that incorporate these additional factors. Initially, a local-in-time theory is developed, covering the existence, uniqueness, and a blow-up criterion under relatively general conditions for these interacting factors. Subsequently, we identify different conditions on the interactions between damping, diffusion, and noise that enable the global regularity and long-time behaviour of classical solutions. Notably, we demonstrate the existence of an evolution system of measures, generalising the concept of invariant measures to the time-inhomogeneous system. |
| title | Damping-Diffusion-Noise Interactions in the Stochastic Camassa--Holm Equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.07649 |