Abstract
It is quite difficult to show the existence and uniqueness of solution for the 3-D Navier-Stokes equations. The difficulty arises from the quadratic two nonlilnear terms, the vortex stretching term and the convection term. In order to see how these two terms affect the existence of the solution, De Gregorio proposed a 1-D model equation for the 3-D vorticity equation. However, in spite of its simple formulation, mathematical analysis of the model is not so easy. Thus, in this article, we investigate the model equation by numerical means, and discuss the property of the solution.
