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arXiv · 2112.03821

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

Javier Gómez-Serrano·Jaemin Park·Jia Shi
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Abstract

In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler equations with compact support but non-concentrated around one 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 our knowledge. The proof relies on a new observation that finite energy, stationary solutions with simply-connected vorticity have compactly supported velocity, and an application of the Nash-Moser iteration procedure.

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Javier Gómez-Serrano, Jaemin Park, Jia Shi. 2021-12-07. Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy. https://arxiv.org/abs/2112.03821

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