  This paper is devoted to the study of nonlinear stability of steady
incompressible Euler flows in two dimensions. We prove that a steady Euler flow
is nonlinearly stable in $L^p$ norm of the vorticity if its stream function is
a semistable solution of some semilinear elliptic problem with strictly
increasing nonlinearity. The idea of the proof is to show that such a flow has
strict local maximum energy among flows whose vorticities are rearrangements of
a given function, with the help of an improvement version of Wolansky and
Ghil's stability theorem. The result can be regarded as an extension of
Arnol'd's second stability theorem.
