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A global existence theorem for the nonlinear BGK equation

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Abstract

A global existence theorem with large initial data inL 1 is given for the nonlinear BGK equation. The method, which is based on the recent averaging lemma of Golseet al., utilizes a weak compactness argument inL 1.

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References

  1. P. L. Bhatnagar, E. P. Gross, and M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,Phys. Rev. 94:511–525 (1954).

    Google Scholar 

  2. P. Welander, On the temperature jump in a rarefied gas,Ark. Fys. 7:507 (1954).

    Google Scholar 

  3. J. Polewczak and W. Greenberg, Some remarks about continuity properties of local Maxwellians and an existence theorem for the BGK model of the Boltzmann equation,J. Stat. Phys. 33:307–316 (1983).

    Google Scholar 

  4. R. L. DiPerna and P. L. Lions, On the Cauchy problem for the Boltzmann equation: Global existence and weak stability, preprint (1988).

  5. F. Golse, P. L. Lions, B. Perthame, and R. Sentis, Regularity of the moments of the solution of a transport equation,J. Funct. Anal. 76:110–125 (1988).

    Google Scholar 

  6. J. Voigt, TheH-theorem for Boltzmann type equations,J. Reine Angew. Math. 326:198–213 (1981).

    Google Scholar 

  7. C. Cercignani,Theory and Application of the Boltzmann Equation (Elsevier, New York, 1975).

    Google Scholar 

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Greenberg, W., Polewczak, J. A global existence theorem for the nonlinear BGK equation. J Stat Phys 55, 1313–1321 (1989). https://doi.org/10.1007/BF01041091

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