1 citations · 2 across the 15 of their papers we have counts for
17 papers
Geometric effects on the persistence of patch structures for 2D Euler equations in simply-connected bounded domains
Emeric Roulley
We first prove a rigidity result for uniformly rotating vortex patch solutions to Euler equations in bounded simply-connected planar domains. Namely, if a bounded simply-connected…
Singular Contour Dynamics and Paradifferential Reduction
Xingyu Li, Emeric Roulley, Stefano Scrobogna
We develop a direct paradifferential approach to nonlinear graph integral operators arising in contour dynamics. The main methodological result is an abstract structure-preserving…
On stationary Quasi-Geostrophic Shallow-Water flows
Vittorio Baroncini, Claudia García, Emeric Roulley
In this paper, we prove the existence of -fold doubly-connected stationary vortex patches for the quasi-geostrophic shallow-water equations. The solutions are obtained…
Quasi-periodic traveling electron layers
Luca Franzoi, Emeric Roulley
We consider the one dimensional space-periodic Vlasov-Poisson equations and construct, close to symmetric flat velocity strips, small amplitude traveling quasi-periodic electron-la…
Ions-electrons-states for the two-component Vlasov-Poisson equation
Emeric Roulley
We establish both local and global bifurcation results for traveling periodic solutions of the one-dimensional two-species Vlasov-Poisson equation. These solutions consist of strip…
Confinement results near point vortices on the rotating sphere
Martin Donati, Emeric Roulley
We study the Euler equation on the rotating sphere in the case where the absolute vorticity is initially sharply concentrated around several points. We follow the literature alread…
Filamentation near monotone zonal vortex caps
Gian Marco Marin, Emeric Roulley
We study the Euler equations on a rotating unit sphere, focusing on the dynamics of vortex caps. Leveraging the -stability of monotone, longitude-independent profiles, we demo…
Long-time dynamics for the Kelvin-Helmholtz equations close to circular vortex sheets
Federico Murgante, Emeric Roulley, Stefano Scrobogna
We consider the Kelvin-Helmholtz system describing the evolution of a vortex-sheet near the circular stationary solution. Answering previous numerical conjectures in the 90s physic…
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…
Uniformly rotating vortices for the lake equation
Taoufik Hmidi, Haroune Houamed, Emeric Roulley +1
We investigate the existence of time-periodic vortex patch solutions, in both simply and doubly-connected cases, for the two-dimensional lake equation where the depth function of t…
Local and global bifurcation of electron-states
Emeric Roulley
We study the bifurcation of traveling periodic electron layers, that we call electron-states, from symmetric and asymmetric flat velocity strips in the phase space, for the one dim…
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…
Periodic and quasi-periodic Euler- flows close to Rankine vortices
Emeric Roulley
In the present contribution, we first prove the existence of -fold simply-connected V-states close to the unit disc for Euler- equations. These solutions are implici…
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…
Vortex rigid motion in quasi-geostrophic shallow-water equations
Emeric Roulley
In this paper, we prove the existence of relative equilibria with holes for quasi-geostrophic shallow-water equations. More precisely, using bifurcation techniques, we establish fo…
Time quasi-periodic vortex patches for quasi-geostrophic shallow-water equations
Taoufik Hmidi, Emeric Roulley
In this paper, we shall implement KAM theory in order to construct a large class of time quasi-periodic solutions for an active scalar model arising in fluid dynamics. More precise…