Abstract
Spherically symmetric solutions to the Cauchy problem for the relativistic Vlasov-Poisson system are studied in three space dimensions. If the energy is positive definite (the plasma physics case), global classical solutions exist. In the case of indefinite energy, “small” radial solutions exist in the large, but “large” data solutions (those with negative energy) will blow-up in finite time.
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Communicated by L. Nirenberg
Research supported in part by NSF MCS 8319944
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Glassey, R.T., Schaeffer, J. On symmetric solutions of the relativistic Vlasov-Poisson system. Commun.Math. Phys. 101, 459–473 (1985). https://doi.org/10.1007/BF01210740
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DOI: https://doi.org/10.1007/BF01210740