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\begin{document}

\title{Global Well-posedness and Asymptotics of Full Compressible Non-resistive
MHD System with Large External Potential Forces}



\author[1]{Wanrong Yang}%
\author[2]{Xiaokui Zhao}%
\affil[1]{North Minzu University}%
\affil[2]{Henan Polytechnic University}%


\vspace{-1em}



  
  \date{May 19, 2024}


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\begin{abstract}
We consider the global well-posedness and asymptotic behavior of
compressible viscous, heat-conductive, and non-resistive
magnetohydrodynamics (MHD) fluid in a field of external forces over
three-dimensional periodic thin domain
\$\textbackslash{}Omega=\textbackslash{}mathbb\{T\}\^{}2\textbackslash{}times(0,\textbackslash{}delta)\$.
The unique existence of the stationary solution is shown under the
adhesion and the adiabatic boundary conditions. Then, it is shown that a
solution to the initial boundary value problem with the same boundary
and periodic conditions uniquely exists globally in time and converges
to the stationary solution as time tends to infinity. Moreover, if the
external forces are small or disappeared in an appropriate Sobolev
space, then \$\textbackslash{}delta\$ can be a general constant. Our
proof relies on the two-tier energy method for the reformulated system
in Lagrangian coordinates and the background magnetic field which is
perpendicular to the flat layer. Compared to the work of Tan and Wang
(SIAM J. Math. Anal. 50:1432--1470, 2018), we not only overcome the
difficulties caused by temperature, but also consider the big external
forces.%
\end{abstract}%



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