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Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior

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  • A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as $|x|\to\infty$ is considered. Hence, the total positive charge and the total negative charge are both infinite. It is shown, in three spatial dimensions, that smooth solutions may be continued as long as the velocity support remains finite. Also, in the case of spherical symmetry, a bound on velocity support is obtained and hence solutions exist globally in time.
    Mathematics Subject Classification: 35L60, 35Q99, 82C21, 82C22, 82D10.

    Citation:

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