تقرير
Leapfrogging vortex rings as scaling limit of Euler Equations
| العنوان: | Leapfrogging vortex rings as scaling limit of Euler Equations |
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| المؤلفون: | Buttà, Paolo, Cavallaro, Guido, Marchioro, Carlo |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, 76B47, 37N10 |
| الوصف: | We consider 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 thickness $\varepsilon$, each one of vorticity mass and main radius of order $|\log\varepsilon|$. When $\varepsilon \to 0$, we show that, at least for small but positive times, the motion of the rings converges to a dynamical system firstly introduced in [NoDEA Nonlinear Diff. Eq. Appl. 6 (1999), 473-499]. In the special case of two vortex rings with large enough main radius, the result is improved reaching longer times, in such a way to cover the case of several overtakings between the rings, thus providing a mathematical rigorous derivation of the leapfrogging phenomenon. Comment: 33 pages, 1 figure; typos corrected, references updated |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.00732 |
| رقم الأكسشن: | edsarx.2310.00732 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |