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In this paper, we study the stability two-dimensional (2D) steady Euler flowswith sharply concentrated vorticity in a simply-connected bounded domain. Theseflows are obtained as maximizers of the kinetic energy subject to theconstraint that the vorticity is compactly supported in a finite number ofdisjoint regions of small diameter. We prove the nonlinear stability of theseflows when the vorticity is concentrated in one small region, or in two smallregions with opposite signs. The proof is achieved by showing that these flowsconstitute a compact and isolated set of local maximizers of the kinetic energyon an isovortical surface. The separation property of the stream function playsa crucial role in validating the isolatedness.

Stability of two-dimensional steady Euler flows with concentrated vorticity