63 citations · 169 across the 18 of their papers we have counts for
20 papers · 1 filter
Uniformly Rotating Euler Configurations with Multiple Vorticity Holes
Vittorio Baroncini, Juan Carlos Cantero, Claudia García +2
We construct new families of uniformly rotating vortex-patch solutions of the two-dimensional incompressible Euler equations consisting of a simply connected outer patch and multip…
Time-periodic leapfrogging vortex rings in the 3D Euler equations
Claudia García, Zineb Hassainia, Taoufik Hmidi
We prove the existence of time-periodic leapfrogging vortex rings for the three-dimensional incompressible Euler equations, thereby providing a rigorous realization of a phenomenon…
Desingularization of time-periodic vortex motion in bounded domains via KAM tools
Zineb Hassainia, Taoufik Hmidi, Emeric Roulley
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…
Rigorous derivation of the leapfrogging motion for planar Euler equations
Zineb Hassainia, Taoufik Hmidi, Nader Masmoudi
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 concentrate…
Axisymmetric Incompressible Viscous Plasmas: Global Well-Posedness and Asymptotics
Diogo Arsénio, Zineb Hassainia, Haroune Houamed
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…
Dynamic Behavior of a Multi-Layer Quasi-Geostrophic Model: Weak and Time-Periodic Solutions
Zineb Hassainia, Haroune Houamed
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 vortici…
Dynamics of vortex cap solutions on the rotating unit sphere
Claudia Garcia, Zineb Hassainia, Emeric Roulley
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 n…
Invariant KAM tori around annular vortex patches for 2D Euler equations
Zineb Hassainia, Taoufik Hmidi, Emeric Roulley
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 b…
Boundary effects on the emergence of quasi-periodic solutions for Euler equations
Zineb Hassainia, Emeric Roulley
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 n…
Time quasi-periodic vortex patches of Euler equation in the plane
Massimiliano Berti, Zineb Hassainia, Nader Masmoudi
We prove the existence of time quasi-periodic vortex patch solutions of the 2-Euler equations in , close to uniformly rotating Kirchhoff elliptical vortices, with…
KAM theory for active scalar equations
Zineb Hassainia, Taoufik Hmidi, Nader Masmoudi
In this paper, we establish the existence of time quasi-periodic solutions to generalized surface quasi-geostrophic equation in the patch form close to Rankine vor…
Multipole vortex patch equilibria for active scalar equations
Zineb Hassainia, Miles H. Wheeler
We study how a general steady configuration of finitely-many point vortices, with Newtonian interaction or generalized surface quasi-geostrophic interactions, can be desingularized…
On the global well-posedness of the 3D axisymmetric resistive MHD equations
Zineb Hassainia
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyz…
Existence of corotating asymmetric vortex pairs for Euler equations
Zineb Hassainia, Taoufik Hmidi
In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence…
Global bifurcation of rotating vortex patches
Zineb Hassainia, Nader Masmoudi, Miles H. Wheeler
We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinit…
An analytical and numerical study of steady patches in the disc
Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi +1
In this paper, we prove the existence of -fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar…
Doubly connected V-states for the generalized surface quasi-geostrophic equations
Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi
In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with They can be described by countable branches bifurcating from…
On the V-states for the generalized quasi-geostrophic equations
Zineb Hassainia, Taoufik Hmidi
We prove the existence of the V-states for the generalized inviscid SQG equations with These structures are special rotating simply connected patches with fold s…
On the inviscid Boussinesq system with rough initial data
Zineb Hassainia, Taoufik Hmidi
We deal with the local well-posedness theory for the two-dimensional inviscid Boussinesq system with rough initial data of Yudovich type. The problem is in some sense critical due…
On the 2D Isentropic Euler System with Unbounded Initial vorticity
Zineb Hassainia
This paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on $\log\varepsilo…