FLUID DYNAMICS RESEARCH 42(2) 025506 (10pp) 2010年4月 [査読有り]
The movement of fluid particles around a running cylinder or a sphere is considered. Particle trajectories viewed from a fixed object are contours of the stream function and well known in many cases. Here, we are concerned with trajectories viewed...
JOURNAL OF MATHEMATICAL FLUID MECHANICS 11(1) 46-59 2009年3月 [査読有り]
The generalized Proudman-Johnson equation, which was derived from the Navier-Stokes equations by Jinghui Zhu and the author, are considered in the case where the viscosity is neglected and the periodic boundary condition is imposed. The equation p...
We present evidence on the global existence of solutions of De Gregorio's equation, based on numerical computation and a mathematical criterion analogous to the Beale-Kato-Majda theorem. Its meaning in the context of a generalized Constantin-...
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 83(7) 114-118 2007年10月 [査読有り]
A parameterized family of continuous functions which was considered by the first author is re-visited in the case when they are monotonically increasing. We prove that the functions are not only continuous and strictly increasing but also singular...
We consider two-dimensional progressive water-waves, which propagate with a constant speed and a constant shape. Fluid motion is assumed to be irrotational. Trajectories in a coordinate system attached to the wave are easily computed by drawing co...