Geometric Regularity Criteria for Incompressible Navier--Stokes Equations with Navier Boundary Conditions

Siran Li

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arXiv · 1802.03535

Geometric Regularity Criteria for Incompressible Navier--Stokes Equations with Navier Boundary Conditions

Siran Li

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Abstract

We study the regularity criteria for weak solutions to the $3D$ incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the boundary effects. A boundary regularity theorem is proved on regular domains with a class of oblique derivative boundary conditions, providing that the vorticity of the fluid is coherently aligned. In particular, we establish the boundary regularity on round balls, half-spaces and right circular cylindrical ducts, subject to the classical Navier and kinematic boundary conditions.

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Siran Li. 2018-02-10. Geometric Regularity Criteria for Incompressible Navier--Stokes Equations with Navier Boundary Conditions. https://arxiv.org/abs/1802.03535

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