We prove the nonlinear asymptotic stability of the gravitational hydrostatic equilibrium for the general equation of state of pressure-density relation in the framework of vacuum free boundary problem of spherically symmetric compressible Navier-Stokes-Poisson equations in three dimensions.The results apply to white dwarfs and polytropes with γ≥2, for which even the linearized asymptotic stability results are not available in literature, to the best of the authors' knowledge. Detailed decay rates of perturbations are given.

In this paper we consider the well-posedness of the compressible Prandtl boundary layer for the Navier–Stokes–Poisson equations with nonslip boundary condition and obtain the linear stability of the approximate solution constructed by boundary layer expansion.

The multi-scale zero relaxation singular limit for gas dynamics in thermal non-equilibrium with multiple non-equilibrium modes in multi-dimensions with physical boundaries from non-equilibrium to thermal equilibrium of compressible Euler flow is proved in this paper for analytical data by establishing the uniform local-in-time estimates. A cancellation mechanism is utilized to deal with the nonlinear singular terms that cause the increase in both time and space derivatives in energy estimates. The rates of the relaxations corresponding to different non-equilibrium modes tending to zero discussed in this paper can be arbitrarily different.

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