4 papers · 1 filter
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…
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…
MHS equilibria in the non-resistive limit to the randomly forced resistive magnetic relaxation equations
Ken Abe, In-Jee Jeong, Federico Pasqualotto +1
We consider randomly forced resistive magnetic relaxation equations (MRE) with resistivity and a force proportional to on the flat -torus for…
Steady Compressible 3D Euler Flows in Toroidal Volumes without Continuous Euclidean Isometries
Naoki Sato, Michio Yamada
We demonstrate the existence of smooth three-dimensional vector fields where the cross product between the vector field and its curl is balanced by the gradient of a smooth functio…