On stationary solutions of two-dimensional Euler equation (Q394008)

The author considers the Euler system for perfect incompressible fluids in a smooth bounded domain \(\Omega\subset {\mathbb R}^d\) and study the stability of steady-state solutions. Among various results he shows that for such a steady-state solution \(\vec v\in (C^1(\Omega))^3\) such that \(c^{-1}<|\vec v|<c\) for a \(c>0\), the streamlines of \(\vec v\) are \(C^{\infty}\) curves. Moreover if \(\vec v\in( C^{3,a}(\Omega))^3\) for \(a>0\), the streamlines are real analytic. The novelty with respect to previous works is that no boundary conditions are prescribed on \(\partial\Omega\).