zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The Vlasov-Maxwell-Boltzmann system in the whole space. (English) Zbl 1129.35022
Author’s abstract: The Vlasov-Maxwell-Boltzmann system is one of the most fundamental models to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove existence of global in time classical solutions to the Cauchy problem near Maxwellians.
MSC:
35F20General theory of first order nonlinear PDE
82D10Plasmas (statistical mechanics)
35Q60PDEs in connection with optics and electromagnetic theory
76P05Rarefied gas flows, Boltzmann equation
35A05General existence and uniqueness theorems (PDE) (MSC2000)
References:
[1]Aoki K., Bardos C., Takata S. (2003) Knudsen layer for gas mixtures. J. Stat. Phys. 112(3–4): 629–655 · Zbl 1124.82314 · doi:10.1023/A:1023876025363
[2]Cercignani, C., Illner, R., Pulvirenti, M.: The mathematical theory of dilute gases. Applied Mathematical Sciences, Vol. 106, New York: Springer-Verlag, 1994
[3]Chapman, S., Cowling, T. G.: The mathematical theory of non-uniform gases. An account of the kinetic theory of viscosity, thermal conduction and diffusion in gases. Third edition, prepared in co-operation with Burnett, D. London: Cambridge University Press, 1970
[4]Desvillettes L., Dolbeault J. (1991) On long time asymptotics of the Vlasov-Poisson-Boltzmann equation. Comm. Partial Differ. Eqs. 16(2–3): 451–489 · Zbl 0737.35127 · doi:10.1080/03605309108820765
[5]Duan, R., Yang, T., Zhu, C.-J.: Global existence to Boltzmann equation with external force in infinite vacuum. To appear in J. Math. Phys.
[6]Glassey, R. T., The Cauchy problem in kinetic theory. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 1996
[7]Glassey R.T., Strauss W.A. (1999) Decay of the linearized Boltzmann–Vlasov system. Transport Theory Statist. Phys. 28(2): 135–156 · Zbl 0983.82018 · doi:10.1080/00411459908205653
[8]Glassey R.T., Strauss W.A. (1999) Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete Contin. Dynam. Systems 5(3): 457–472 · Zbl 0951.35102 · doi:10.3934/dcds.1999.5.457
[9]Guo Y. (2001) The Vlasov–Poisson–Boltzmann system near vacuum. Commun. Math. Phys. 218(2): 293–313 · doi:10.1007/s002200100391
[10]Guo Y. (2002) The Vlasov–Poisson–Boltzmann system near Maxwellians. Comm. Pure Appl. Math. 55(9): 1104–1135 · Zbl 1027.82035 · doi:10.1002/cpa.10040
[11]Guo Y. (2003) The Vlasov–Maxwell–Boltzmann system near Maxwellians. Invent. Math. 153(3): 593–630 · Zbl 1029.82034 · doi:10.1007/s00222-003-0301-z
[12]Guo Y. (2004) The Boltzmann equation in the whole space. Indiana Univ. Math. J. 53(4): 1081–1094 · Zbl 1065.35090 · doi:10.1512/iumj.2004.53.2574
[13]Lions, P.-L.: Global solutions of kinetic models and related questions. In: Nonequilibrium problems in many-particle systems (Montecatini, 1992), Lecture Notes in Math. 1551, Berlin: Springer, 1993, pp. 58–86
[14]Liu T.-P., Yu S.-H. (2004) Boltzmann equation: micro-macro decompositions and positivity of shock profiles. Commun. Math. Phys. 246(1): 133–179 · Zbl 1092.82034 · doi:10.1007/s00220-003-1030-2
[15]Liu T.-P., Yang T., Yu S.-H. (2004) Energy method for Boltzmann equation. Phys. D 188(3–4): 178–192 · Zbl 1098.82618 · doi:10.1016/j.physd.2003.07.011
[16]Mischler S. (2000) On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system. Commun. Math. Phys. 210(2): 447–466 · Zbl 0983.45007 · doi:10.1007/s002200050787
[17]Strain R.M., Guo Y. (2004) Stability of the relativistic Maxwellian in a Collisional Plasma. Commun. Math. Phys. 251(2): 263–320 · Zbl 1113.82070 · doi:10.1007/s00220-004-1151-2
[18]Strain R.M., Guo Y. (2006) Almost Exponential Decay Near Maxwellian. Commun. Partial Differ. Eqs. 31(3): 417–429 · Zbl 1096.82010 · doi:10.1080/03605300500361545
[19]Yang, T., Yu, H., Zhao, H.: Cauchy Problem for the Vlasov–Poisson–Boltzmann System. To appear in Arch. Rational Mech. Anal., 42 pages, available at http://www.math.ntnu.no/conservation/2004/027.pdf
[20]Yang, T., Zhao, H.: Global Existence of Classical Solutions to the Vlasov–Poisson–Boltzmann System. Commun. Math. Phys., to appear. DOI 10.1007/s00220-006-0103-4
[21]Villani, C.: A review of mathematical topics in collisional kinetic theory. Handbook of mathematical fluid dynamics, Vol. I, Amsterdam: North Holland, 2002, pp. 71–305