Weak Solutions to the Stationary Incompressible Euler Equations

Abstract

We consider weak stationary solutions to the incompressible Euler equations and show that the analogue of the $h$-principle obtained by the second author in joint work with C. De Lellis for time-dependent weak solutions in $L^\infty$ continues to hold. The key difference arises in dimension d=2, where it turns out that the relaxation set is strictly smaller than what one obtains in the time-dependent case.