International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3319-3346

Construction of axisymmetric steady states of an inviscid incompressible fluid by spatially discretized equations for pseudo-advected vorticity

Takahiro Nishiyama1

1Department of Intelligent Mechanical Engineering, Faculty of Engineering, Fukuoka Institute of Technology, Fukuoka 8110295, Japan
2Department of Applied Science, Faculty of Engineering, Yamaguchi University, Ube 7558611, Japan

Received 18 April 2005

Copyright © 2005 Takahiro Nishiyama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An infinite number of generalized solutions to the stationary Euler equations with axisymmetry and prescribed circulation are constructed by applying the finite difference method for spatial variables to an equation of pseudo-advected vorticity. They are proved to be different from exact solutions which are written with trigonometric functions and a Coulomb wave function.