9 citations · 12 across the 4 of their papers we have counts for
4 papers
Existence of vortex rings in Beltrami flows
Ken Abe
We construct traveling wave solutions to the 3d Euler equations by axisymmetric Beltrami fields with a non-constant proportionality factor. They form a vortex ring with nested inva…
On the large time -estimates of the Stokes semigroup in two-dimensional exterior domains
Ken Abe
We prove that the Stokes semigroup is a bounded analytic semigroup on of angle for two-dimensional exterior domains. This result is an end point case of the $L…
Stability of Lamb dipoles
Ken Abe, Kyudong Choi
The Lamb dipole is a traveling wave solution to the two-dimensional Euler equations introduced by S. A. Chaplygin (1903) and H. Lamb (1906) at the early 20th century. We prove orbi…
The vorticity equations in a half plane with measures as initial data
Ken Abe
We consider the two-dimensional Navier-Stokes equations subject to the Dirichlet boundary condition in a half plane for initial vorticity with finite measures. We study local well-…