On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
Abstract
In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension d\geq 4 , axisymmetric, swirl-free solutions of the Euler equation have properties which could allow finite-time singularity formation of a form that is excluded when d=3 , and we prove a conditional blowup result for axisymmetric, swirl-free solutions of the Euler equation in dimension d\geq 4 . The condition which must be imposed on the solution in order to imply blowup becomes weaker as d\to +\infty , suggesting the dynamics are becoming much more singular as the dimension increases.
Fields of Study & Subjects
Navier-Stokes equation solutions
Computational Fluid Dynamics and Aerodynamics
Fluid Dynamics and Turbulent Flows
Publication details
- Journal / source
- Revista Matemática Iberoamericana
- Volume
- 42
- Issue
- 5
- Pages
- 1681–1726
- Publication date
- 6 March 2026
- Language
- EN