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On a Vlasov–Poisson Plasma with Infinite Charge and Velocities

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 209))

Abstract

In this article I will overview some recent results on the Vlasov and the Vlasov–Poisson equations, for a given initial particle distribution which is not \(L^1\) in space and has infinite support in the velocities.

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References

  1. Caprino, S., Cavallaro, G., Marchioro, C.: On a magnetically confined plasma with infinite charge. SIAM J. Math. Anal. 46, 133–164 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Caprino, S., Cavallaro, G., Marchioro, C.: Remark on a magnetically confined plasma with infinite charge. Rend. Mat. Appl. 35, 69–98 (2014)

    MathSciNet  MATH  Google Scholar 

  3. Caprino, S., Cavallaro, G., Marchioro, C.: Existence and uniqueness of the time evolution for a plasma with infinite charge in \(\mathbb{R} ^3\). Commun. Partial Differ. Equ. 40, 1–29 (2015)

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  4. Caprino S., Cavallaro G., Marchioro C.: A Vlasov–Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror (To appear on Kin. Rel. Mod)

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  5. Caprino S., Cavallaro G., Marchioro C.: The Vlasov–Poisson equation in \(\mathbb{R} ^3\) with infinite charge and velocities (Submitted to Commun. Partial Differ. Equ.)

    Google Scholar 

  6. Glassey, R.: The Cauchy problem in kinetic theory. SIAM, Philadelphia (1996)

    Book  MATH  Google Scholar 

  7. Lions, P.L., Perthame, B.: Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105, 415–430 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pfaffelmoser, K.: Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Differ. Equ. 95, 281–303 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Schaeffer, J.: Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Commun. Partial Differ. Equ. 16(8–9), 1313–1335 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Silvia Caprino .

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Caprino, S. (2017). On a Vlasov–Poisson Plasma with Infinite Charge and Velocities. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations. PSPDE 2015. Springer Proceedings in Mathematics & Statistics, vol 209. Springer, Cham. https://doi.org/10.1007/978-3-319-66839-0_3

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