Global Strong Solutions to the One-Dimensional Planar Compressible Magneto-Micropolar Equations with Vacuum
- 1College of Science, China Agricultural University, Beijing 100083, China
Abstract
We consider the one-dimensional planar isentropic compressible magneto-micropolar equations on a bounded interval, with homogeneous Dirichlet boundary conditions and initial data that may contain vacuum, the initial density being allowed to vanish on an open subset of the interval. For large initial data satisfying four natural compatibility conditions, we prove the global existence and uniqueness of strong solutions. The proof rests on a priori estimates in which the magnetic and micro-rotation couplings are controlled by the dissipation, through a coercive functional built from material-derivative testing and a density bound that requires no positive lower bound. To the best of our knowledge, this is the first global well-posedness result, with vacuum and large initial data, for the compressible magneto-micropolar equations in one space dimension.
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BibTeX
@article{shi2026global,
title = {{Global Strong Solutions to the One-Dimensional Planar Compressible Magneto-Micropolar Equations with Vacuum}},
author = {Pan Shi},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213893},
url = {https://www.mdpi.com/2227-7390/14/21/3893},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Global Strong Solutions to the One-Dimensional Planar Compressible Magneto-Micropolar Equations with Vacuum
AU - Pan Shi
PY - 2026
DA - 2026/10/25
JO - Mathematics
DO - 10.3390/math14213893
UR - https://www.mdpi.com/2227-7390/14/21/3893
AB - We consider the one-dimensional planar isentropic compressible magneto-micropolar equations on a bounded interval, with homogeneous Dirichlet boundary conditions and initial data that may contain vacuum, the initial density being allowed to vanish on an open subset of the interval. For large initial data satisfying four natural compatibility conditions, we prove the global existence and uniqueness of strong solutions. The proof rests on a priori estimates in which the magnetic and micro-rotation couplings are controlled by the dissipation, through a coercive functional built from material-derivative testing and a density bound that requires no positive lower bound. To the best of our knowledge, this is the first global well-posedness result, with vacuum and large initial data, for the compressible magneto-micropolar equations in one space dimension.
SN - 2227-7390
ER -