We consider the Cauchy problem for the equations of selfgravitating motions of a barotropic gas with density-dependent viscosities μ(ρ), and λ(ρ) satisfying the Bresch-Desjardins condition, when the pressure P(ρ) is not necessarily a monotone function of the density. We prove that this problem admits a global weak solution provided that the adiabatic exponent γ associated with P(ρ) satisfiesγ > 4/3.
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