Global large solutions for one-dimensional nematic liquid crystal system with initial vacuum

This paper is concerned with a one-dimensional compressible nematic liquid crystal system with large initial data. We proved the global existence and uniqueness of strong solutions to the Cauchy problem when the initial density permits the presence of internal vacuum and far-field vacuum. Moreover, under weaker initial density conditions, we show the conclusion when the initial vacuum can be permitted inside the region. In order to obtain the uniform upper bounds on the density, the flow graph Lagrangian coordinates, mathematical frequency decomposition techniques and some weighted energy estimates are introduced.