Abstract
We prove the blow-up in finite time for sherically symmetric solutions to the Euler-Poisson system with repulsive forces. We show that a “gentle” solution with initially bounded support can exist only for a finite time if its initial energy is large (in comparison with its mass). The method is to compare estimates on the inertial moment and on the characteristic curves.
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Perthame, B. Non-existence of global solutions to Euler-Poisson equations for repulsive forces. Japan J. Appl. Math. 7, 363–367 (1990). https://doi.org/10.1007/BF03167849
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DOI: https://doi.org/10.1007/BF03167849