三次元渦度方程式の一次元モデルDe Gregorio方程式の数値的研究(理論,科学技術計算と数値解析,<特集>平成18年研究部会連合発表会)

概要

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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.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.
日本応用数理学会の論文
2006-09-25