14 citations · 18 across the 6 of their papers we have counts for
6 papers
Enstrophy variations in the collapsing process of point vortices
Takeshi Gotoda
We investigate enstrophy variations by collapse of point vortices in an inviscid flow and, in particular, focus on the enstrophy dissipation that is a significant property characte…
Energy conservation in the limit of filtered solutions for the 2D Euler equations
Takeshi Gotoda
We consider energy conservation in a two-dimensional incompressible and inviscid flow through weak solutions of the filtered-Euler equations, which describe a regularized Euler flo…
Self-similar motions and related relative equilibria in the -point vortex system
Takeshi Gotoda
We study self-similar solutions of the point-vortex system. The explicit formula for self-similar solutions has been obtained for the three point-vortex problem and for a specific…
Convergence of filtered weak solutions to the 2D Euler equations with vortex sheet initial data
Takeshi Gotoda
We study weak solutions of the two-dimensional (2D) filtered Euler equations whose vorticity is a finite Radon measure and velocity has locally finite kinetic energy, which is call…
Universality of the anomalous enstrophy dissipation at the collapse of three point vortices on Euler-Poincaré models
Takeshi Gotoda, Takashi Sakajo
Anomalous enstrophy dissipation of incompressible flows in the inviscid limit is a significant property characterizing two-dimensional turbulence. It indicates that the investigati…
Global solvability and convergence of the Euler-Poincaré regularization of the two-dimensional Euler equations
Takeshi Gotoda
We study the Euler-Poincaré equations that are the regularized Euler equations derived from the Euler-Poincaré framework. It is noteworthy to remark that the Euler-Poincaré equatio…