On a One‐Component Blow‐Up Criterion for Inhomogeneous Axially Symmetric Navier–Stokes Equations
Abstract
ABSTRACT We prove a critical Prodi–Serrin‐type regularity criterion depending only on the azimuthal component of the vorticity for the inhomogeneous axisymmetric Navier–Stokes system, with or without allowance of the vacuum. More precisely, if then a strong solution to the inhomogeneous axisymmetric Navier–Stokes system can be extended regularly beyond . The result is valid in the case of large variations of density with possible vacuum. Moreover, if we exclude the possibility of vacuum, the aforementioned criterion also works for . Furthermore, a discussion on the case of is also provided, and a subcritical single‐component criterion, with a ‐order gap, is shown in the Appendix.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Volume
- 49
- Issue
- 8
- Pages
- 8425–8435
- Publication date
- 18 January 2026
- Language
- EN