Integral geometry of Euler equations

Abstract

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.

22 pages; Theorem 5.1 in versions 2-7 being wrong, the main result is conditional