Global well-posedness for the planar compressible Hall-magnetohydrodynamic equations with density-dependent viscosity

This paper is concerned with the planar compressible Hall-magnetohydrodynamic equations with large initial data. We study a free boundary problem and assume that the viscosity coefficient depends on the density in the form of ρα. The existence of unique global strong solution to the free boundary problem is proven for 0<α<13. The proof relies on the skew-symmetric structure of the Hall term and the connection between energy estimates in Eulerian and Lagrangian coordinates.