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The existence of global in time weak solutions to theNavier-Stokes-Poisson system of barotropic compressibleflow is proved. The system takes into account the effect ofself-gravitation. Moreover, the case of a non-monotone pressureimportant in certain applications in astrophysics and the theoryof nuclear fluids is included.
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Ducomet et al. (2004) studied this question.
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