Ibrahim Suleiman

Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations

Let $m \ge 4$. We prove that there is a forward orbit of the 2D Euler system for scale-invariant $m$-fold symmetric vorticities, namely \begin{equation*} \partial_tg + 2G\partial_\theta g = 0, \quad 4G + \partial_{\theta\theta}G = g, \end{equation*} which is dense in $S :=\{g \in L_{m,\mathrm{odd}}^\infty(\mathbb{S}^1)...