Abstract
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) satisfies \({\gamma > \frac{4}{3}}\).
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Ducomet, B., Nečasová, Š. & Vasseur, A. On global motions of a compressible barotropic and selfgravitating gas with density-dependent viscosities. Z. Angew. Math. Phys. 61, 479–491 (2010). https://doi.org/10.1007/s00033-009-0035-x
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DOI: https://doi.org/10.1007/s00033-009-0035-x