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In this paper, we study an initial value problem of the Navier-Stokes-Poisson equations for compressible, viscous, heat-conducting flows on the whole space R 3 . The global well-posedness of strong solutions subject to large and non-flat doping profile is established. The initial data is of small energy but possible large oscillations, and the initial density is allowed to contain vacuum states. [ABSTRACT FROM AUTHOR]

This paper concerns an initial value problem of compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in whole space R 3. The global well-posedness of strong solutions with large oscillations and vacuum is established, provided the initial data are of small energy and the steady state is strictly away from vacuum. A weak-strong uniqueness result is also obtained. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]