  In this paper, we investigate nonlinear stability of planar steady Euler
flows related to least energy solutions of the Lane-Emden equation in a smooth
bounded domain. We prove the orbital stability of these flows in terms of both
the $L^s$ norm of the vorticity for any $s\in(1,+\infty)$ and the energy norm.
As a consequence, nonlinear stability is obtained when the least energy
solution is unique, which actually holds for a large class of domains and
exponents. The proofs are based on a new variational characterization of least
energy solutions in terms of the vorticity, a compactness argument, and proper
use of conserved quantities of the Euler equation.
