Global axisymmetric solution to the 3D incompressible inhomogeneous Navier–Stokes equations
Abstract
In this paper, we prove the existence and uniqueness of a global axisymmetric solution to the three-dimensional (3D) incompressible inhomogeneous Navier–Stokes equations. The system is posed in an infinite cylindrical domain and is complemented with the Navier boundary condition. We pay special attention to the case where the friction coefficient is $ \alpha = 0 $. In this case, the horizontal diffusion of the swirl component becomes particularly weak due to the failure of Korn's inequality. To overcome this challenge, we introduce several novel quantities and establish new CKN-type inequalities, which are vital for closing the energy estimates.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 54
- Issue
- 0
- Pages
- 87–112
- Publication date
- 1 January 2026