Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Hassainia , Zineb"'
We examine the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the single poi
Externí odkaz:
http://arxiv.org/abs/2408.16671
The main goal of this paper is to explore the leapfrogging phenomenon in the inviscid planar flows. We show for 2d Euler equations that under suitable constraints, four concentrated vortex patches leapfrog for all time. When observed from a translati
Externí odkaz:
http://arxiv.org/abs/2311.15765
Autor:
Hassainia, Zineb, Houamed, Haroune
The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their respective
Externí odkaz:
http://arxiv.org/abs/2309.17202
Publikováno v:
Forum of Mathematics, Sigma 12 (2024) e79
This paper is devoted to the global analysis of the three-dimensional axisymmetric Navier--Stokes--Maxwell equations. More precisely, we are able to prove that, for large values of the speed of light $c\in (c_0, \infty)$, for some threshold $c_0>0$ d
Externí odkaz:
http://arxiv.org/abs/2309.12060
In this work, we analytically study the existence of periodic vortex cap solutions for the homogeneous and incompressible Euler equations on the rotating unit 2-sphere, which was numerically conjectured by Dritschel-Polvani and Kim-Sakajo-Sohn. Such
Externí odkaz:
http://arxiv.org/abs/2306.00154
We construct time quasi-periodic vortex patch solutions with one hole for the planar Euler equations. These structures are captured close to any annulus provided that its modulus belongs to a massive Borel set. The proof is based on Nash-Moser scheme
Externí odkaz:
http://arxiv.org/abs/2302.01311
Publikováno v:
In Journal of Differential Equations 5 February 2025 417:1-63
Autor:
Hassainia, Zineb, Roulley, Emeric
In this paper, we highlight the importance of the boundary effects on the construction of quasi-periodic vortex patches solutions close to Rankine vortices and whose existence is not known in the whole space due to the resonances of the linear freque
Externí odkaz:
http://arxiv.org/abs/2202.10053
We prove the existence of time quasi-periodic vortex patch solutions of the 2$d$-Euler equations in $\mathbb{R}^2$, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full Lebesgue measu
Externí odkaz:
http://arxiv.org/abs/2202.06215
In this paper, we establish the existence of time quasi-periodic solutions to generalized surface quasi-geostrophic equation $({\rm gSQG})_\alpha$ in the patch form close to Rankine vortices. We show that invariant tori survive when the order $\alpha
Externí odkaz:
http://arxiv.org/abs/2110.08615