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