9 citations · 12 across the 4 of their papers we have counts for
8 papers · 1 filter
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-…
Liouville theorems for the Stokes equations with applications to large time estimates
Ken Abe
We study Liouville theorems for the non-stationary Stokes equations in exterior domains in under decay conditions for spatial variables. As applications, we prove…
Vanishing viscosity limits for axisymmetric flows with boundary
Ken Abe
We construct global weak solutions of the Euler equations in an infinite cylinder for axisymmetric initial data without sw…