Šverák's conjecture on non-precompact vorticity orbits

Let $M\subset\mathbb{R}^2$ be a bounded planar domain, let $\omega_0\in L^{\infty}(M)$ be initial vorticity, and let $\{\omega(t)\}_{t\in\mathbb{R}}$ be its inviscid incompressible Euler orbit. Šverák's conjecture. Generic initial data give rise to motions whose vorticity orbits are not precompact in $L^2(M)$. The precise meaning of genericity is left open in the source; the conjecture formalizes the creation of small scales or mixing at infinite time.