On the Two-Dimensional Euler Equations with Spatially Almost Periodic Initial Data

Abstract

We consider the nonstationary Euler equations in R 2 with almost periodic unbounded vorticity. We show that a unique solution is always spatially almost periodic at any time when the almost periodic initial data belongs to some function space. In order to prove this, we demonstrate the continuity with respect to initial data which do not decay at spatial infinity. The proof of the continuity with respect to initial data is based on that of Vishik's uniqueness theorem.

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