4 problems

Let $omega_0$ be an initial vorticity and let $Omega_+(\omega_0)$ denote its $omega$-limit set. Consider a configuration of $n$ fixed-shape vortex blobs whose centers of mass inter…

Let $omega_0$ be an initial vorticity and let … be its $omega$-limit set. For initial data $omega$ in this set, further mixing means a loss of the conserved-orbit enstrophy, measur…

Let $omega_0$ be an initial vorticity, let $S_t(\omega_0)$ be the corresponding Euler flow, and define the $omega$-limit set by … Here the closure is taken in the weak- topology. S…

Šverák's conjecture. For generic $omega_0\in L^\infty(\mathbb{S}^2)$, the orbit $\{S_t(\omega_0)\mid t\geq 0\}$ is not precompact in $L^2$. This is interpreted as a mathematical fo…