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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…
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…