2 problems

Generic flow-map non-precompactness conjecture. For a residual subset of $\mathcal{U}_p$, the associated flow maps $\{\Phi_t\}_{t\geq 0}$ are not precompact in $L^1$.

Let $H$ be the left half of the torus, and let $\Psi$ be the flow generated by an incompressible vector field $u$. The image of $H$ under the flow $\Psi$ after time $T$ is called…