Abstract
We consider the Cauchy problem for the equations of spherically symmetric motions in \({\mathbb {R}^3}\), of a selfgravitating barotropic gas, with possibly non monotone pressure law, in two different situations: in the first one we suppose that the viscosities μ(ρ), and λ(ρ) are density-dependent and satisfy the Bresch–Desjardins condition, in the second one we consider constant densities. In the two cases, we prove that the problem admits a global weak solution, provided that the polytropic index γ satisfy γ > 1.
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Communicated by H. Beirao da Veiga
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Ducomet, B., Nečasová, Š. & Vasseur, A. On Spherically Symmetric Motions Of a Viscous Compressible Barotropic and Selfgravitating Gas. J. Math. Fluid Mech. 13, 191–211 (2011). https://doi.org/10.1007/s00021-009-0010-5
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DOI: https://doi.org/10.1007/s00021-009-0010-5