9 citations · 29 across the 15 of their papers we have counts for
15 papers
Existence of homogeneous Euler flows of degree
Ken Abe
We consider ()-homogeneous solutions to the stationary incompressible Euler equations in for and in for . Shvydk…
Stability of Chandrasekhar's nonlinear force-free fields
Ken Abe
Chandrasekhar's nonlinear force-free field, discovered in 1956, is a rare example of a nonlinear force-free field describing a large coherent structure of axisymmetric magnetic fie…
Rigidity of Beltrami fields with a non-constant proportionality factor
Ken Abe
We prove that bounded Beltrami fields must be symmetric if a proportionality factor depends on 2 variables in the cylindrical coordinate and admits a regular level set diffeomorphi…
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…