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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2108.13223 |
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| _version_ | 1866909531974402048 |
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| author | Rumpf, Benno Soffer, Avy Tran, Minh-Binh |
| author_facet | Rumpf, Benno Soffer, Avy Tran, Minh-Binh |
| contents | We analyse a 3-wave kinetic equation, derived from the elastic beam wave equation on the lattice. The ergodicity condition states that two distinct wavevectors are supposed to be connected by a finite number of collisions. In this work, we prove that the ergodicity condition is violated and the equation domain is broken into disconnected domains, called no-collision and collisional invariant regions. If one starts with a general initial condition, whose energy is finite, then in the long-time limit, the solutions of the 3-wave kinetic equation remain unchanged on the no-collision region and relax to local equilibria on the disjoint collisional invariant regions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13223 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the wave turbulence theory: ergodicity for the elastic beam wave equation Rumpf, Benno Soffer, Avy Tran, Minh-Binh Analysis of PDEs We analyse a 3-wave kinetic equation, derived from the elastic beam wave equation on the lattice. The ergodicity condition states that two distinct wavevectors are supposed to be connected by a finite number of collisions. In this work, we prove that the ergodicity condition is violated and the equation domain is broken into disconnected domains, called no-collision and collisional invariant regions. If one starts with a general initial condition, whose energy is finite, then in the long-time limit, the solutions of the 3-wave kinetic equation remain unchanged on the no-collision region and relax to local equilibria on the disjoint collisional invariant regions. |
| title | On the wave turbulence theory: ergodicity for the elastic beam wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2108.13223 |