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arXiv · 2209.10022

Spatially quasi-periodic solutions of the Euler equation

Xu Sun·Peter Topalov
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Abstract

We develop a framework for studying quasi-periodic maps and diffeomorphisms on $\mathbb{R}^n$. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on $\mathbb{R}^n$. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.

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Xu Sun, Peter Topalov. 2022-09-20. Spatially quasi-periodic solutions of the Euler equation. https://doi.org/10.1007/s00021-023-00804-9

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