Electron. J. Differential Equations, Vol. 2025 (2025), No. 58, pp. 1-29
Global unique solution for 3D incompressible inhomogeneous magneto-micropolar equations with discontinuous density
Xiao Song, Chenhua Wang, Xiaojie Wang, Fuyi Xu
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 2, 2025.
Math Subject Classifications: 35Q35, 35A01, 35A02.
Key Words: Discontinuous density; global well-posedness; critical Besov space; magneto-micropolar equation.
DOI: 10.58997/ejde.2025.58
Show me the PDF file (450 KB),
TEX file for this article.
| |
Xiao Song
School of Mathematics and Statistics
Shandong University of Technology
Zibo Shandong 255049, China
email: ssxnsong@163.com
|
|---|
| |
Chenhua Wang
School of Mathematics and Statistics
Shandong University of Technology
Zibo Shandong, 255049, China
email: wangchenhua 2024@163.com
|
|---|
| |
Xiaojie Wang
School of Mathematics and Statistics
Shandong University of Technology
Zibo Shandong 255049, China
email: wxj15615637750@163.com
|
|---|
 |
Fuyi Xu
School of Mathematics and Statistics
Shandong University of Technology
Zibo Shandong 255049, China
email: zbxufuyi@163.com
|
|---|
Return to the EJDE web page