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• W3099681847 abstract "When the velocity field is not a priori known to be globally almost Lipschitz, global uniqueness of solutions to the two-dimensional Euler equations has been established only in some special cases, and the solutions to which these results apply share the property that the diffuse part of the vorticity is constant near the points where the velocity is insufficiently regular. Assuming that the latter holds initially, the challenge is then to propagate this property along the Euler dynamic via an appropriate control of the Lagrangian trajectories. In domains with obtuse corners and sufficiently smooth elsewhere, Yudovich solutions fail to be almost Lipschitz only near these corners, and we investigate the necessary and sufficient conditions for the vorticity to remain constant there. We show that if the vorticity is initially constant near the whole boundary, then it remains so forever (and global weak solutions are unique), provided that no corner has angle greater than $$pi $$ . We also show that this fails in general for domains that do have such corners." @default.
• W3099681847 created "2020-11-23" @default.
• W3099681847 creator A5059199669 @default.
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• W3099681847 date "2019-05-02" @default.
• W3099681847 modified "2023-09-27" @default.
• W3099681847 title "The Euler Equations in Planar Domains with Corners" @default.
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• W3099681847 doi "https://doi.org/10.1007/s00205-019-01384-7" @default.
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