2 citations · 5 across the 8 of their papers we have counts for
8 papers
Continuation and reduction of steady vortex sheets under metric deformations on a disk
Yuuki Shimizu
We study the local continuation of a steady vortex sheet under a prescribed deformation of a conformal metric on the unit disk. Representing the movin…
Hydrodynamic Killing vector fields on surfaces
Yuuki Shimizu
Killing vector fields, which have their origins in Riemannian geometry, have recently garnered attention for their significance in understanding fluid flows on curved surfaces. Owi…
Numerical analysis for the Plateau problem by the method of fundamental solutions
Koya Sakakibara, Yuuki Shimizu
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our…
Locality of vortex stretching for the 3D Euler equations
Yuuki Shimizu, Tsuyoshi Yoneda
We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely…
Mathematical justification of the point vortex dynamics in background fields on surfaces as an Euler-Arnold flow
Yuuki Shimizu
The point vortex dynamics in background fields on surfaces is justified as an Euler-Arnold flow in the sense of de Rham currents. We formulate a current-valued solution of the Eule…
Point vortex on surfaces with continuous symmetry
Yuuki Shimizu
We derive an analytic formula for the hydrodynamic Green function and the Robin function on every orientable surface admitting a hydrodynamic Killing vector field. Closed-form expr…
On the asymptotic behavior of Bessel-like diffusions
Yuuki Shimizu, Fumihiko Nakano
We derive the asymptotic behavior of the transition probability density of the Bessel-like diffusions for "dimension" .
A remark on conditions that a diffusion in the natural scale is a martingale
Yuuki Shimizu, Fumihiko Nakano
We consider a diffusion processes on an interval in the natural scale. Some results are known under which is a martingale, and we give simple and analytic p…