90 citations · 472 across the 43 of their papers we have counts for
4 papers · 2 filters
Unified theory on V-states structures for active scalar equations
Taoufik Hmidi, Liutang Xue, Zhilong Xue
This paper revolves around the existence of V-states close to Rankine vortices for active scalar equations with completely monotone kernels. This allows to unify various results on…
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…
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…
Time periodic solutions close to localized radial monotone profiles for the 2D Euler equations
Claudia García, Taoufik Hmidi, Joan Mateu
In this paper, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type , w…