The system of the Navier-Stokes equations at the vorticity level on the two dimensional manifolds

Subject Areas : هندسه

Mahsa Abbasvand ¹ , Hajar Ghahremani-Gol ²

1 - Department of Mathematics, Faculty of Science, Shahed University, Tehran P.C. 3319118651 , Iran
2 - Department of Mathematics, Faculty of Science, Shahed University, Tehran P.C. 3319118651 , Iran

Received: 2022-05-23 Accepted : 2023-10-17 Published : 2024-11-30

Keywords: پیچش, معادلات ناویر استوکس, دیورژانس, خمینه ریمانی,

Abstract :

The system of the Navier - Stokes equation is one of the basic equations in mathematics that plays a major role in aerodynamics , geophysics and some engineering sciences. In the Euclidean space $\mathbb{R}^{n}$ , the existence and the properties of the solutions of the Navier - Stokes equation as well as its modeling have been extensively researched in practical matters. These equations at the vorticity level are also very important for the study of vortex theory and some physical phenomena. In the recent years , investigation on the system of the Navier - Stokes equation has been considered when the fluid region is a Riemannian manifold. In this paper, we obtain the vorticity flows on two - dimensional Riemannian equations, including the two - dimensional sphere, Finally we calculate the solutions of the f the vorticity flows on the two - dimensional sphere and then we simulate some of these solutions.

References:


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