“…These results were extended to some related systems by Chen, Young, and Zhang [5], such as MHD equations and compressible Euler equations for the fluid in variable area ducts. To the subject of fluid near vacuum (or containing vacuum), we refer the readers to [2,14,21,22]. To the weak solutions of hyperbolic conservation laws, we refer the readers to [6,8,10,14,20,25,26,27].…”