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In this paper, we prove the existence of locally non-radial solutions to thestationary 2D Euler equations with compact support but non-concentrated aroundone or several points. Our solutions are of patch type, have analytic boundary,finite energy and sign-changing vorticity and are new to the best of ourknowledge. The proof relies on a new observation that finite energy, stationarysolutions with simply-connected vorticity have compactly supported velocity,and an application of the Nash-Moser iteration procedure.

Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy