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Boundary effects on the emergence of quasi-periodic solutions for Euler equations

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arxiv 2202.10053 v1 pith:JM5XSVUH submitted 2022-02-21 math.AP physics.flu-dyn

Zineb Hassainia , Emeric Roulley This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords boundaryeffectsequationseulerexistencequasi-periodicrankinesolutions
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In this paper, we highlight the importance of the boundary effects on the construction of quasi-periodic vortex patches solutions close to Rankine vortices and whose existence is not known in the whole space due to the resonances of the linear frequencies. Availing of the lack of invariance by radial dilation of Euler equations in the unit disc and using a Nash-Moser implicit function iterative scheme we show the existence of such structures when the radius of the Rankine vortex belongs to a suitable massive Cantor-like set with almost full Lebesgue measure.

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  1. Existence of analytic non-convex V-states

    math.AP 2024-11 conditional novelty 8.0 of 10

    A rigorous computer-assisted proof establishes the existence of non-convex analytic uniformly rotating vortex patches with 6-fold symmetry for the 2D Euler equation.

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