Stability of the 2D Boussinesq‐MHD System With Fractional Horizontal Dissipation
Abstract
ABSTRACT This paper investigates the stability of perturbations near equilibrium states for the two‐dimensional Boussinesq‐magnetohydrodynamics (MHD) system with fractional horizontal dissipation in the domain , where is the one‐dimensional periodic box. The absence of vertical dissipation, combined with the presence of fractional operators, presents significant challenges to the study of stability and long‐time dynamics in the Boussinesq‐MHD system. To address these issues, we leverage the orthogonal decomposition method in conjunction with multiple fractional anisotropic interpolation inequalities and a fractional Poincaré‐type inequality within our analytical framework. We prove the global stability of the system when the initial data are sufficiently small in .
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Publisher
- Wiley
- Volume
- 49
- Issue
- 8
- Pages
- 8357–8382
- Publication date
- 8 January 2026
- Language
- EN