Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 58, pp. 1-29

Title: Global unique solution for 3D incompressible inhomogeneous magneto-micropolar equations with discontinuous density

Authors: Xiao Song (Shandong Univ. of Technology, Zibo Shandong, China)
         Chenhua  Wang (Shandong Univ. of Technology, Zibo Shandong, China)
         Xiaojie  Wang (Shandong Univ. of Technology, Zibo Shandong, China)
         Fuyi Xu (Shandong Univ. of Technology, Zibo Shandong, China)

Abstract:
This article concerns the Cauchy problem of the incompressible
inhomogeneous  magneto-micropolar equations in $\mathbb{R}^3$. 
We first prove the global solvability of the model  when the initial 
density is bounded from above and below with positive constants and 
the initial velocity, angular velocity, and magnetic field in a critical 
Besov spaces  are sufficiently small. 
Then we  obtain the Lipschitz regularity for the fluid velocity, 
magnetic field, and angular velocity by exploiting some extra
time-weighted energy estimates. We show the uniqueness of the 
constructed global solutions by the duality approach.
 

Submitted December 22, 2024. Published June 02, 2025.
Math Subject Classifications: 35Q35, 35A01, 35A02.
Key Words: Discontinuous density; global well-posedness; critical Besov space; magneto-micropolar equation.