4 papers
Uniformly Rotating Euler Configurations with Multiple Vorticity Holes
Vittorio Baroncini, Juan Carlos Cantero, Claudia GarcÃa +3
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 GarcÃa, 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…
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…
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…