9 citations · 18 across the 17 of their papers we have counts for
17 papers
On ideal lemniscates, butterflies, and circular waves
Shinya Okabe, Glen Wheeler
We prove the existence of infinitely many lemniscate-like, butterfly-like, and circular-wave critical points for the length-penalised ideal energy. For the lemniscate and butterfly…
Well-posedness of the Langmuir film problem
Yoichiro Mori, Shinya Okabe, Koya Sakakibara
We analyze the inviscid Langmuir layer--Stokesian subfluid (ILLSS) model for two-phase Langmuir monolayers coupled to a Stokes flow in the underlying subfluid. Eliminating the bulk…
A Sobolev gradient flow for the area-normalised Dirichlet energy of maps
Shinya Okabe, Philip Schrader, Valentina Wheeler +1
In this article we study the -gradient flow for the energy where is the Dirichlet energy of , is the signedenclosed area of , and $X…
An obstacle problem for the p-elastic energy
Anna Dall'Acqua, Marius Müller, Shinya Okabe +1
In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler--Lagrange equa…
Convergence of Sobolev gradient trajectories to elastica
Shinya Okabe, Philip Schrader
In this paper we study the -gradient flow for the modified elastic energy defined on closed curves in . We prove the existence of a unique global-in-time sol…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…