三维可压缩液晶在有界区域上强解的整体存在性和大时间行为

his paper mainly studies the initial boundary value problem of a compressible simplified version of Ericksen Leslie system in a three-dimensional bounded domain. The global existence and large time behavior of strong solutions for compressible liquid crystal models on bounded regions are obtained when the initial value is close to a equilibrium state in $H^2$ Sobolev space. Initially, the energy method is employed to derive low--order energy estimates for the solution and high--order energy estimates within the interior of the domain. Subsequently, utilizing the boundary flattening technique, high--order energy estimates near the boundary are deduced in a new local coordinate system. Finally, based on the existing local solutions and derived prior estimates, the local solutions are extended to the global solution, thereby proving the global existence and long-term behavior of strong solutions for compressible liquid crystal models on bounded regions.