Global stability and asymptotic behavior for incompressible ideal MHD equations with velocity damping term

2025/12/29 by Hui Fang, Fang, Hui, Pingping Gui +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems

paper · doi:10.48550/arxiv.2512.23263

Abstract

In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the Diophantine condition. Our results mathematically characterize the background magnetic field exerts the stabilizing effect, and bridge the gap left by previous work with respect to the asymptotic behavior in time. Our proof approach mainly relies on the Fourier analysis and energy estimates. In addition, we provide a versatile analytical framework applicable to many other partially dissipative fluid models.

Citations

• Global stability and asymptotic behavior for the incompressible MHD equations without viscosity or magnetic diffusion
• Asymptotic stability for n-dimensional isentropic compressible MHD equations without magnetic diffusion
• Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion
• Stability for the 2D incompressible MHD equations with only magnetic diffusion
• Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain
• Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator
• Singularity formation in the incompressible Euler equation in finite and infinite time
• Asymptotic Behaviors of Global Solutions to the Two-Dimensional Non-resistive MHD Equations with Large Initial Perturbations
• On the exponential stability of a stratified flow to the 2D IDEAL MHD equations with damping
• On the global solution of 3-D MHD system with initial data near equilibrium
• Local existence for the non-resistive MHD equations in Besov spaces
• Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
• Global small solution to the 2D MHD system with a velocity damping term

Related

• Global stability and asymptotic behavior for the incompressible MHD equations without viscosity or magnetic diffusion
• Global small solution to the 2D MHD system with a velocity damping term
• Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium
• Stability for the 2D incompressible MHD equations with only magnetic diffusion
• Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion