We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"–"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions.

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linearly equivalent to a large constant state. There is no restriction on the size of the initial velocity and micro-rotational velocity. As a byproduct, we prove the exponential decay for the solution.