2021
DOI: 10.48550/arxiv.2106.08288
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2D point vortex dynamics in bounded domains: global existence for almost every initial data

Abstract: In this paper, we prove that in bounded planar domains with C 2,α boundary, for almost every initial condition in the sense of the Lebesgue measure, the point vortex system has a global solution, meaning that there is no collision between two pointvortices or with the boundary. This extends the work previously done in [13] for the unit disk. The proof requires the construction of a regularized dynamics that approximates the real dynamics and some strong inequalities for the Green's function of the domain. In t… Show more

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Cited by 1 publication
(3 citation statements)
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“…In the case of the Euler equations in a bounded simply connected smooth connected domain of R 2 with impermeability condition at the boundary, it is possible to proceed to an analogous construction [7] and get…”
Section: Point-vortex For the Euler Equationsmentioning
confidence: 99%
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“…In the case of the Euler equations in a bounded simply connected smooth connected domain of R 2 with impermeability condition at the boundary, it is possible to proceed to an analogous construction [7] and get…”
Section: Point-vortex For the Euler Equationsmentioning
confidence: 99%
“…Proof. A direct computation using the evolution equations for the point-vortex problem in bounded domains under developed form (7) gives…”
Section: Evolution In Time Of the Studied Distributionmentioning
confidence: 99%
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