Spatially Quasi-Periodic Solutions of the Euler Equation

We develop a framework for studying quasi-periodic maps and diffeomorphisms on R-n. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on 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.

Automated summary

We propose a framework for studying quasi-periodic maps and diffeomorphisms on R-n. As an application, we prove the local well-posedness of the Euler equation in a space of quasi-periodic vector fields on R-n. Specifically, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and initial data are demonstrated.