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

2025/08/04 by Zhang, Zhibing, Zu, Qian
#35A02 #35B53 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.02449

Abstract

In this paper, we investigate Liouville type theorems for the 3D stationary magneto-micropolar fluid equations. Adopting an iterative procedure, taking advantage of the special structure of the equations and using a novel combination of two different interpolation inequalities, we establish Liouville type theorems if the smooth solution satisfies certain growth conditions in terms of L^p-norms on the annuli. Compared with the velocity field 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. Besides, we also obtain Liouville type theorems for the 3D stationary micropolar fluid equations.

Citations

• New Liouville type theorems for 3D steady incompressible MHD equations and Hall-MHD equations
• Some remarks about the stationary Micropolar fluid equations: existence, regularity and uniqueness
• Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids
• Liouville type theorems for stationary Navier-Stokes equations
• Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces
• Sufficient conditions on Liouville type theorems for the 3D steady Navier-Stokes equations

Related

• Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids
• New Liouville type theorems for 3D steady incompressible MHD equations and Hall-MHD equations
• Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids
• Regularity criteria of 3D generalized magneto-micropolar fluid system in terms of the pressure
• Liouville-type theorems for the planer stationary MHD equations with growth at infinity