Long-time dynamics conjecture for generic solutions of the 2D Euler equation

Let solutions of the two-dimensional Euler equation evolve as $t\to\pm\infty$. A solution is called generic in the informal sense intended by the conjecture, and its weak limit set is the set of weak accumulation points of its trajectory. Long-time dynamics conjecture. As $t\rightarrow\pm\infty$, generic solutions experience loss of compactness, and the weak limit set of generic solutions consists only of solutions lying on compact orbits. This informal conjecture describes the expected relaxation of most smooth enough solutions of the two-dimensional Euler equation toward simpler dynamics. The supplied text gives no resolution, and the precise meaning of genericity and the asserted long-time behavior remain open.