2 problems

Let $u=\nabla^\perp\psi$ be a steady Euler solution in a periodic channel, with an interior critical streamline $\Gamma_0$ and vorticity $\omega=F(\psi)$ for analytic $F$. Suppose…

Let $\Omega\subset\mathbb{R}^3$ be a toroidal domain, meaning that $\partial\Omega$ is diffeomorphic to $\mathbb{T}^2$. A smooth steady Euler flow on $\Omega$ is a smooth solution…