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On the statistical solutions of Vlasov-Poisson equations in two dimensions

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Abstract

We investigate the problem of the uniqueness of the statistical solutions of the Vlasov-Poisson equations for an electron plasma in a two dimensional torus.

Zusammenfassung

Wir untersuchen die Frage nach der Eindeutigkeit statistischer Lösungen der Vlasov-Poisson-Gleichung für eln Eiektronenplasma im räumlich zweidimensionalen periodischen Fall.

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References

  1. A. A. Arsenev,On the existence of statistical solutions of the Vlasov system of equations. Sov. Math. Dok.16, 216–218 (1975).

    Google Scholar 

  2. C. Foias,Statistical study of Navier-Stokes equations I. Rend. Sem. Mat. Univ. Padova48, 220–348 (1973); II49, 9–123 (1973).

    Google Scholar 

  3. C. Foias and R. Temam,Self-similar universal homogeneous statistical solutions of the Navier-Stokes equation. Comm. Math. Phys.90, 187–206 (1983)

    Google Scholar 

  4. E. Hopf,Statistical Hydromechanics and Functional Calculus. J. Rat. Mech. Anal.1, 87–121 (1952).

    Google Scholar 

  5. E. Horst,On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation. Math. Meth. Appl. Sci.3, 229–248 (1981).

    Google Scholar 

  6. M. Pulvirenti and J. Wick,Convergence of Galerkin approximation for two-dimensional Vlasow-Poisson equation. Z. angew. Math. Phys.35, 790–801 (1984).

    Google Scholar 

  7. H. Spohn,Lecture given at the international summerschool “Kinetic Theories and Boltzmann Equations” of C. I. M. E. in Montecatini (Italy). June 1981.

  8. H. Spohn,On the Vlasov Hierarchy. Math. Meth. Appl. Sci.3, 445–455 (1981).

    Google Scholar 

  9. L. Schwartz,Radon measures on arbitrary topological spaces and cylindrical measures. Oxford 1973.

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Pulvirenti, M., Wick, J. On the statistical solutions of Vlasov-Poisson equations in two dimensions. Z. angew. Math. Phys. 36, 508–519 (1985). https://doi.org/10.1007/BF00945293

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  • DOI: https://doi.org/10.1007/BF00945293

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