Time evolution of vortex rings with large radius and very concentrated vorticity
@inproceedings{Cavallaro2021TimeEO, title={Time evolution of vortex rings with large radius and very concentrated vorticity}, author={Guido Cavallaro and Carlo Marchioro}, year={2021} }
We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii ≈ r0 and thickness ε. We prove that when r0 = | log ε|α, α > 2, the vorticity field of the fluid converges as ε → 0 to the point vortex model, at least for a small but positive time. This result generalizes a previous paper that assumed a power law for the relation between r0 and ε.
2 Citations
Global time evolution of concentrated vortex rings
- Mathematics, PhysicsZeitschrift für angewandte Mathematik und Physik
- 2022
We study the time evolution of an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside N small disjoint rings of…
Stability of the two-dimensional point vortices in Euler flows
- Mathematics
- 2022
∂tω + u · ∇ω = 0 ω(0, x) = ω0(x). We are interested in the cases when the initial vorticity has the form ω0 = ω0,ǫ + ω0p,ǫ, where ω0,ǫ is concentrated near M disjoint points p0m and ω0p,ǫ is a small…
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