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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 250, Pages 219–225 (Mi tm39)  

This article is cited in 5 scientific papers (total in 5 papers)

Kinetic Equations and the Chapman–Enskog Projection Problem

E. V. Radkevich

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (158 kB) Citations (5)
References:
Abstract: It is well known that in the low-frequency cutoffs of the Chapman–Enskog projection of moment approximations of the Boltzmann kinetic equation, the so-called ultraviolet catastrophe occurs. For the first time, this phenomenon was pointed out by A. V. Bobylev in 1992 in the simplest mode (of one-dimensional linear deviation from global equilibrium). By an example of moment approximation of the Boltzmann–Peierls kinetic equation, we prove the existence of a Chapman–Enskog projection to the phase space of the conservative variable in the class of first-order hyperbolic pseudodifferential systems with relaxation. This result is used to explain the phenomenon of ultraviolet catastrophe.
Received in January 2005
Bibliographic databases:
UDC: 517.9+533.7
Language: Russian
Citation: E. V. Radkevich, “Kinetic Equations and the Chapman–Enskog Projection Problem”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 250, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 219–225; Proc. Steklov Inst. Math., 250 (2005), 204–210
Citation in format AMSBIB
\Bibitem{Rad05}
\by E.~V.~Radkevich
\paper Kinetic Equations and the Chapman--Enskog Projection Problem
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 250
\pages 219--225
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm39}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2200916}
\zmath{https://zbmath.org/?q=an:1138.82351}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 204--210
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  • https://www.mathnet.ru/eng/tm39
  • https://www.mathnet.ru/eng/tm/v250/p219
  • This publication is cited in the following 5 articles:
    1. I. V. Zagrebaev, “A Mixed Problem for the Dirac–Schwinger Extension of the Maxwell System”, Math. Notes, 91:2 (2012), 172–186  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. I. V. Zagrebaev, E. V. Radkevich, “On intermediate attractors”, Journal of Mathematical Sciences, 190:1 (2013), 80–103  mathnet  crossref  mathscinet
    3. V. V. Palin, “Solvability of matrix Riccati equations”, J. Math. Sci. (N. Y.), 163:2 (2009), 176–187  mathnet  crossref  mathscinet  zmath  elib
    4. E. V. Radkevich, “Matrix Equations and the Chapman–Enskog Projection”, Proc. Steklov Inst. Math., 261 (2008), 229–236  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Palin, VV, “Hyperbolic regularizations of conservation laws”, Russian Journal of Mathematical Physics, 15:3 (2008), 343  crossref  mathscinet  zmath  adsnasa  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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