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arXiv · 2508.00189

Long-time evolution of forced waves in the low viscosity regime

Nicolas Frantz·Michał Wrochna
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Abstract

We consider a model for internal waves described by a zero order pseudo-differential Hamiltonian $P$ damped by a second order viscosity term $i \nu Q$. 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 $\nu$ regime. We show that dissipation effects arise no earlier than at the $t\sim \nu^{-1/3-}$ time scale.

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Nicolas Frantz, Michał Wrochna. 2025-07-31. Long-time evolution of forced waves in the low viscosity regime. https://arxiv.org/abs/2508.00189

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