On the Cauchy problem of compressible full Hall-MHD equations

This paper is concerned with an initial value problem of the compressible full Hall-MHD equations in three-dimensional whole space. Both the global existence and the optimal decay rates of solutions are obtained, when the smooth initial data are sufficiently close to the non-vacuum equilibrium in $H^1$. As a by-product of the uniform estimates, the vanishing limit of Hall coefficient is also justified.