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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…
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…