The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem
- Seiji Ukai
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A technique based on the abstract Cauchy-Kovalevskaya theorem is used to derive uniform estimates of solutions of BBGKY hierarchy, which improves Lanford’s theorem on the Boltzmann-Grad limit and simplifies its proof, in part. It is also applied to the Euler limit of the Boltzmann hierarchy.
- K. Aoki, C. Bardos, F. Golse and Y. Sone, Derivations of hydrodynamic limits from either the Liouville equation or kinetic models: Study of examples. Kokyuroku (eds. A. Matsumura and S. Kawasima), RIMS, Kyoto Univ., 2000, 154–181.
- K. Asano, Local solutions to the initial and initial-boundary value problem for the Boltzmann equation with an external force, I. J. Math. Kyoto Univ.,24 (1984), 225–238.
- C. Cercignani, R. Illner and M. Pluvirenti, The Mathematical Theory of Dilute Gases. Appl. Math. Sci.109, Springer-Verlag, New York-Berlin, 1994.
- H. Grad, On the kinetic theory of rarefied gases. Comm. Pure Appl. Math.,2 (1949), 331–407. CrossRef
- O. Lanford III, Time evolution of large classical system. Lec. Notes in Phys.38 (ed. E.J. Moser), Springer-Verlag, New York, 1975, 1–111.
- T. Nishida, A note on the theorem of Nierenberg. J. Diff. Geometry,112 (1977), 629–633.
- T. Nishida, Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation. Comm. Math. Phys.,61 (1978), 119–148. CrossRef
- S. Ukai and K. Asano, The Euler limit and initial layer of the Boltzmann equation. Hokkaido Math. J.,12 (1983), 311–332.
- The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem
Japan Journal of Industrial and Applied Mathematics
Volume 18, Issue 2 , pp 383-392
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- Newton equation
- Boltzmann equation
- BBGKY hierarchy
- Boltzmann-Grad limit
- abstract Cauchy-Kovalevskaya theorem
- Seiji Ukai (1)
- Author Affiliations
- 1. Department of Applied Mathematics, Yokohama National University, 79-5 Tokiwadai, Hodogaya, 240-8501, Yokohama, Japan