Analysis of a numerical scheme for 3-wave kinetic equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915764466876416 |
|---|---|
| author | Tran, Minh-Binh Wang, Bangjie |
| author_facet | Tran, Minh-Binh Wang, Bangjie |
| contents | Several numerical schemes for 3-wave kinetic equations have been proposed in recent work and shown to be accurate and computationally efficient [8,33,34,35]. However, their rigorous numerical analysis remains open. This paper aims to close this gap. We establish a comprehensive well-posedness and qualitative theory for the
discrete equation arising from those schemes. We prove
global existence, uniqueness, and Lipschitz stability of nonnegative classical solutions
in $\ell^1(\mathbb{N})$, together with uniform bounds and decay of moments. We further
show exponential energy decay and a sharp creation and propagation of positivity
characterized by the arithmetic structure of the initial support. Finally, we obtain
the propagation and instantaneous creation of polynomial, Mittag-Leffler, and
exponential moments, providing quantitative control of high energy tails. We validate the theoretical findings by numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analysis of a numerical scheme for 3-wave kinetic equations Tran, Minh-Binh Wang, Bangjie Numerical Analysis Several numerical schemes for 3-wave kinetic equations have been proposed in recent work and shown to be accurate and computationally efficient [8,33,34,35]. However, their rigorous numerical analysis remains open. This paper aims to close this gap. We establish a comprehensive well-posedness and qualitative theory for the discrete equation arising from those schemes. We prove global existence, uniqueness, and Lipschitz stability of nonnegative classical solutions in $\ell^1(\mathbb{N})$, together with uniform bounds and decay of moments. We further show exponential energy decay and a sharp creation and propagation of positivity characterized by the arithmetic structure of the initial support. Finally, we obtain the propagation and instantaneous creation of polynomial, Mittag-Leffler, and exponential moments, providing quantitative control of high energy tails. We validate the theoretical findings by numerical results. |
| title | Analysis of a numerical scheme for 3-wave kinetic equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2602.00264 |