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Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425-448, 1969) and Larson (Mon Not R Astr Soc 145:271-295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state , , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson-Penston solution.
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