Long-time evolution of forced waves in the low viscosity regime
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918109465542656 |
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| author | Frantz, Nicolas Wrochna, Michał |
| author_facet | Frantz, Nicolas Wrochna, Michał |
| contents | We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i νQ$. Under Morse-Smale or similar weaker global conditions on the classical dynamics, we describe qualitatively the long-time behavior of solutions of the corresponding evolution equation with smooth forcing in a small $ν$ regime. We show that dissipation effects arise no earlier than at the $t\sim ν^{-1/3-}$ time scale. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time evolution of forced waves in the low viscosity regime Frantz, Nicolas Wrochna, Michał Analysis of PDEs Mathematical Physics Spectral Theory We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i νQ$. Under Morse-Smale or similar weaker global conditions on the classical dynamics, we describe qualitatively the long-time behavior of solutions of the corresponding evolution equation with smooth forcing in a small $ν$ regime. We show that dissipation effects arise no earlier than at the $t\sim ν^{-1/3-}$ time scale. |
| title | Long-time evolution of forced waves in the low viscosity regime |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2508.00189 |