5 papers
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…
Fast relaxation of a viscous vortex in an external flow
Martin Donati, Thierry Gallay
We study the evolution of a concentrated vortex advected by a smooth, divergence-free velocity field in two space dimensions. In the idealized situation where the initial vorticity…
Long-time Confinement near Special Vortex Crystals
Martin Donati
In this paper, we control the growth of the support of particular solutions to the Euler two-dimensional equations, whose vorticity is concentrated near special vortex crystals. Th…
On the dynamics of leapfrogging vortex rings
Martin Donati, Lars Eric Hientzsch, Christophe Lacave +1
The evolution of highly concentrated vorticity around rings in the three-dimensional axisymmetric Euler equations is studied in a regime for which the leapfrogging dynamics predict…
Dynamics of helical vortex filaments in non viscous incompressible flows
Martin Donati, Christophe Lacave, Evelyne Miot
In this paper we study concentrated solutions of the three-dimensional Euler equations in helical symmetry without swirl. We prove that any helical vorticity solution initially con…