8 papers
Admissible Invariant-Torus Foliations for Steady Euler Flows
Naoki Sato, Ken Abe
In 1965, V. I. Arnold established a structure theorem guaranteeing the existence of a foliation by invariant surfaces for general three-dimensional steady Euler flows with non-cons…
Stability for multiple Lamb dipoles
Ken Abe, In-Jee Jeong, Yao Yao
In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are suf…
Minus one Homogeneous Euler Flows are Geodesible
Ken Abe, Naoki Sato, Chunjing Xie
In this paper, we study -homogeneous steady solutions to the Euler equations on . In low dimensions , such flows are known to be essentia…
Existence and stability of Sadovskii vortices: from patch to smooth vortices
Ken Abe, Kyudong Choi, In-Jee Jeong +2
We establish a scaling-invariant variational framework for steadily translating dipoles of the two-dimensional incompressible Euler equations. Specifically, we consider the maximiz…
Homogeneous steady states for the generalized surface quasi-geostrophic equations
Ken Abe, Javier Gómez-Serrano, In-Jee Jeong
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant , representing the 2D…
Topological Invariants in Higher-Dimensional Magnetohydrodynamics
Naoki Sato, Ken Abe, Michio Yamada
It is well known that the three-dimensional ideal magnetohydrodynamics (MHD) equations possess three magnetic invariants: (M) magnetic helicity, (C) cross helicity, and (P) the mea…