On the existence of almost-periodic solutions for the 2D dissipative Euler equations

Abstract

In this paper we study the two-dimensional dissipative Euler equations in a smooth and bounded domain. In the presence of a sufficiently large dissipative term (or equivalently a sufficiently small external force) precise uniform estimates on the modulus of continuity of the vorticity are proved. These allow us to show existence of Stepanov almost-periodic solutions.