In this article we study quasi-geostrophic point-vortex systems in a general setting called alpha point-vortex. We study a particular case of vortex collapses called mono-scale collapses and this study gives the Hölder regularity for the -vortex problem. This result implies in particular that the trajectories of the vortices are convergent even in the case of a collapse.
Accepté le :
Publié le :
Ludovic Godard-Cadillac 1
CC-BY 4.0
@article{CRMATH_2023__361_G1_355_0,
author = {Ludovic Godard-Cadillac},
title = {H\"older estimate for the 3 point-vortex problem with alpha-models},
journal = {Comptes Rendus. Math\'ematique},
pages = {355--362},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
year = {2023},
doi = {10.5802/crmath.414},
language = {en},
}
Ludovic Godard-Cadillac. Hölder estimate for the 3 point-vortex problem with alpha-models. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 355-362. doi : 10.5802/crmath.414. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.414/
[1] Motion of three vortices, Phys. Fluids, Volume 22 (1979) no. 3, pp. 393-400 | DOI | Zbl
[2] Self-similar motion of three point vortices, Phys. Fluids, Volume 22 (2010) no. 5, 057104 | Zbl
[3] Mathematical methods of classical mechanics, Graduate Texts in Mathematics, 60, Springer, 1978 | Numdam | Zbl
[4] Collapse of generalized Euler and surface quasi-geostrophic point-vortices, Phys. Rev. E, Volume 98 (2018) no. 2, 023110 | DOI
[5] Two-Dimensional Point Vortex Dynamics in Bounded Domains: Global Existence for Almost Every Initial Data, SIAM J. Math. Anal., Volume 54 (2022) no. 1, pp. 79-113 | DOI | MR | Zbl
[6] Hölder regularity for collapses of point vortices (2022) (https://arxiv.org/abs/2111.14230)
[7] Point vortices for inviscid generalized surface quasi-geostrophic models, Discrete Contin. Dyn. Syst., Ser. B, Volume 25 (2020) no. 7, pp. 2583-2606 | MR | Zbl
[8] Quasi-geostrophic vortices and their desingularization, Ph. D. Thesis, Sorbonne Université, Paris, France (2020) (in french)
[9] Vortex collapses for the Euler and Quasi-Geostrophic models, Discrete Contin. Dyn. Syst., Volume 42 (2022) no. 7, pp. 3143-3168 | DOI | MR | Zbl
[10] Spezielle Probleme über die Bewegung Geradlinier Paralleler Wirbelfäden, Druck von Zürcher und Furrer (1877) | Zbl
[11] Burst of Point-Vortices and non-uniqueness of 2D Euler equations (2020) (https://arxiv.org/abs/2011.13329)
[12] Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen, J. Reine Angew. Math., Volume 55 (1858), pp. 25-55 | DOI
[13] Finite-time Collapse of Three Point Vortices in the Plane, Regul. Chaotic Dyn., Volume 23 (2018) no. 5, pp. 530-550 | DOI | MR | Zbl
[14] Vortex methods in two-dimensionnal fluid mechanics, Lecture Notes in Physics, 203, Springer, 1984 | Zbl
[15] Mathematical theory of incompressible nonviscous fluids, Applied Mathematical Sciences, 96, Springer, 1994 | DOI | Zbl
[16] The N-vortex problem, analytical techniques, Applied Mathematical Sciences, 145, Springer, 2001 | DOI | Zbl
[17] Dynamics and statistics of a system of vortices, Zh. Eksp. Teor. Fiz., Volume 41 (1975) no. 5, pp. 937-943
[18] Self-similar collapse of three geophysical vortices, Geophys. Astrophys. Fluid Dyn., Volume 115 (2021) no. 4, pp. 369-392 | DOI | MR | Zbl
[19] Self-similar collapse of three vortices in the generalised Euler and quasi-geostrophic equations, Physica D, Volume 434 (2022), 133226 | MR | Zbl
Cité par Sources :
Commentaires - Politique