On strong solutions of Navier-Stokes equations with two velocity components
Abstract
In this paper, we established a continuation criterion for local strong solutions to the three-dimensional incompressible Navier-Stokes equations based on partial velocity components. More precisely, we showed that a unique local strong solution $ u $ does not blow up at time $ T $ provided that the two horizontal velocity components $ u_h $ belong to the Banach spaces $ \dot{V}_{p, q, \theta}^s $ and $ \dot{U}_{p, \beta, \sigma}^s $. These functional spaces strictly contained the homogeneous Besov space $ \dot{B}_{p, q}^s $, and thus allowed a wider admissible class than those considered in earlier works. Our results can therefore be viewed as an extension and refinement of previously known criteria.
Fields of Study & Subjects
Navier-Stokes equation solutions
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 4
- Pages
- 9334–9346
- Publication date
- 1 January 2026