\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Local existence of compressible MHD equations without initial
compatibility conditions}



\author[1]{Yiying Zhang}%
\author[2]{Zhenhua Guo}%
\author[1]{Li Fang}%
\affil[1]{Northwest University School of Mathematics}%
\affil[2]{Guangxi University School of Mathematics and Information Science}%


\vspace{-1em}



  
  \date{June 08, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
In this paper, we study the initial-boundary value problem of
three-dimensional viscous, compressible, and heat conductive
magnetohydrodynamic equations. Local existence and uniqueness of strong
solutions is established with any such initial data that the initial
compatibility conditions do not be required. The analysis is based on
some suitable prior estimates for the strong coupling term \emph{u}\selectlanguage{ngerman}·\selectlanguage{english}[?]
\emph{H} and strong nonlinear term curl H x H . Our proof of the
existence and uniqueness of solutions is in the Lagrangian coordinates
first and then transformed back to the Euler coordinates.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

