Integral geometry of Euler equations

We develop an integral geometry of stationary Euler equations defining some function $w$ on the Grassmannian of affine lines in the space. This function depends on a putative compactly supported solution $v$ of the system, and we deduce a linear differential equation for $w$. We prove also that the purported annulation of $w$ implies that locally supported solutions of the steady Euler equation in $\mathbb R^3$ are zero.