arXiv subjects

Qian Zu

Publications and source records attributed to Qian Zu.

2 recordsLinked to original sources

arXiv2026

Stabilizing effect of a background magnetic field on the 2D damped wave-type MHD equations

The stabilizing effect of a background magnetic field on electrically conducting fluids has been rigorously established for the standard MHD equations. This paper extends this theory to the more physically accurate damped wave-type MHD equations, where the induction equation is hyperbolic-parabolic and the velocity field has only vertical damping with no dissipation. These two features make the stability analysis harder than in the standard MHD setting. To overcome these difficulties, we design an energy functional exploiting the anisotropic structure, and discover a remarkable cancellation between the two most dangerous nonlinear terms by exploiting the full algebraic structure of the coupled system. As a consequence, we prove that any small perturbation near the background magnetic field is globally stable and establish optimal decay rates consistent with the 2D heat equation. To the best of our knowledge, this is the first rigorous stability result for the damped wave-type MHD equations near a background magnetic field.

math.AP↗

arXiv2025

Some new Liouville type theorems for the 3D stationary magneto-micropolar fluid equations

In this paper, we investigate Liouville type theorems for the 3D stationary magneto-micropolar fluid equations and micropolar fluid equations. Adopting an iteration procedure, taking advantage of the special structure of the equations and using a novel combination of interpolation techniques, we establish Liouville type theorems if the smooth solution satisfies certain growth conditions in terms of $L^p$-norms on the annuli. Furthermore, combining the energy method and some subtle ODE analysis, we relax the growth conditions on the velocity field and the magnetic field by logarithmic factors and obtain logarithmic improvement of Liouville type theorems. Compared with the velocity and the magnetic field, we raise the most relaxed restriction for the angular velocity. More specifically, we allow $L^q$-norm of the angular velocity on the annuli to grow polynomially at any degree, i.e. $\|\omega\|_{L^q(B_{2R}\backslash B_{3R/2})}$ is permitted to grow as fast as $R^N$ at infinity, where $N$ is an arbitrary positive integer.

math.AP↗