The Regularity Criteria and the A Priori Estimate on the 3D Incompressible Navier-Stokes Equations in Orthogonal Curvilinear Coordinate Systems. (13th October 2020)

• Record Type: Journal Article
• Authors: Geng, Fan; Wang, Shu; Wang, Yongxin
• Other Names: Wang Fanglei Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-10-13
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/2816183
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The paper considers the regularity problem on three-dimensional incompressible Navier-Stokes equations in general orthogonal curvilinear coordinate systems. We establish one regularity criteria of the weak solutions involving only in a vorticity component ω 3 and one a priori estimate on the solution that H 3 u 3 L ∞ 0, T ; L p ℝ 3 is bounded for 1 ≤ p ≤ ∞ to three-dimensional incompressible Navier-Stokes equations in orthogonal curvilinear coordinate systems. These extent greatly the corresponding results on axisymmetric cylindrical flow.