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Volumn 107, Issue 13, 2010, Pages 5744-5749

Global classical solutions of the Boltzmann equation with long-range interactions

Author keywords

Anisotropy; Fractional derivatives; Kinetic theory; Non cut off

Indexed keywords

ARTICLE; COMPREHENSION; ENTROPY; GEOMETRY; MATHEMATICAL MODEL; PHYSICAL MODEL; PRIORITY JOURNAL;

EID: 77950530316     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1001185107     Document Type: Article
Times cited : (66)

References (32)
  • 1
    • 0004205706 scopus 로고
    • Translated by Stephen G. Brush (Univ of California Press, Berkeley)
    • Boltzmann Ludwig (1964) Lectures on Gas Theory, Translated by Stephen G. Brush (Univ of California Press, Berkeley).
    • (1964) Lectures on Gas Theory
    • Ludwig, B.1
  • 3
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • DiPerna RJ, Lions P-L (1989) On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Ann of Math 130:321-366.
    • (1989) Ann of Math , vol.130 , pp. 321-366
    • Diperna, R.J.1    Lions, P.-L.2
  • 4
    • 12844275468 scopus 로고    scopus 로고
    • On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
    • DOI 10.1007/s00222-004-0389-9
    • Desvillettes L, Villani C (2005) On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation. Invent Math 159:245-316. (Pubitemid 40166695)
    • (2005) Inventiones Mathematicae , vol.159 , Issue.2 , pp. 245-316
    • Desvillettes, L.1    Villani, C.2
  • 5
    • 67649344144 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • North-Holland, Amsterdam
    • Villani Cédric (2002) A review of mathematical topics in collisional kinetic theory. Handbook of Mathematical Fluid Dynamics, (North-Holland, Amsterdam), Vol I, pp 71-305.
    • (2002) Handbook of Mathematical Fluid Dynamics , vol.1 , pp. 71-305
    • Cédric, V.1
  • 6
    • 33644808362 scopus 로고    scopus 로고
    • Almost exponential decay near Maxwellian
    • Strain Robert M, Guo Yan (2006) Almost exponential decay near Maxwellian. Comm Part Diff Eq 31:417-429.
    • (2006) Comm Part Diff Eq , vol.31 , pp. 417-429
    • Strain Robert, M.1    Yan, G.2
  • 7
    • 0036133764 scopus 로고    scopus 로고
    • On the Boltzmann equation for long-range interactions
    • Alexandre R, Villani C (2002) On the Boltzmann equation for long-range interactions. Comm Pure Appl Math 55(1):30-70.
    • (2002) Comm Pure Appl Math , vol.55 , Issue.1 , pp. 30-70
    • Alexandre, R.1    Villani, C.2
  • 10
    • 0002000765 scopus 로고
    • General existence and uniqueness proof for spatially homogeneous solutions of the Maxwell-Boltzmann equation in the case of Maxwellian molecules
    • Morgenstern Dietrich (1954) General existence and uniqueness proof for spatially homogeneous solutions of the Maxwell-Boltzmann equation in the case of Maxwellian molecules. Proc Natl Acad Sci USA 40:719-721.
    • (1954) Proc Natl Acad Sci USA , vol.40 , pp. 719-721
    • Dietrich, M.1
  • 11
    • 0040330066 scopus 로고
    • Sur la théorie de l'équation intégrodiffé rentielle de Boltzmann
    • French
    • Carleman Torsten (1933) Sur la théorie de l'équation intégrodifférentielle de Boltzmann. Acta Math 60:91-146 French.
    • (1933) Acta Math , vol.60 , pp. 91-146
    • Torsten, C.1
  • 12
    • 0000824099 scopus 로고
    • On the existence of global solutions of mixed problem for non-linear Boltzmann equation
    • Ukai Seiji (1974) On the existence of global solutions of mixed problem for non-linear Boltzmann equation. P Japan Acad 50:179-184.
    • (1974) P Japan Acad , vol.50 , pp. 179-184
    • Seiji, U.1
  • 13
    • 34250139505 scopus 로고
    • The Boltzmann equation: Global existence for a rare gas in an infinite vacuum
    • Illner Reinhard, Shinbrot Marvin (1984) The Boltzmann equation: Global existence for a rare gas in an infinite vacuum. Commun Math Phys 95:217-226.
    • (1984) Commun Math Phys , vol.95 , pp. 217-226
    • Reinhard, I.1    Marvin, S.2
  • 14
    • 0041413233 scopus 로고    scopus 로고
    • The Vlasov-Maxwell-Boltzmann system near Maxwellians
    • Guo Yan (2003) The Vlasov-Maxwell-Boltzmann system near Maxwellians. Invent Math 153:593-630.
    • (2003) Invent Math , vol.153 , pp. 593-630
    • Yan, G.1
  • 15
    • 0042438264 scopus 로고    scopus 로고
    • Classical solutions to the Boltzmann equation for molecules with an angular cutoff
    • Guo Yan (2003) Classical solutions to the Boltzmann equation for molecules with an angular cutoff. Arch Rational Mech Anal 169:305-353.
    • (2003) Arch Rational Mech Anal , vol.169 , pp. 305-353
    • Yan, G.1
  • 16
    • 0346498040 scopus 로고    scopus 로고
    • Energy method for Boltzmann equation
    • Liu Tai-Ping, Yang Tong, Yu Shih-Hsien (2004) Energy method for Boltzmann equation. Physica D 188:178-192.
    • (2004) Physica D , vol.188 , pp. 178-192
    • Tai-Ping, L.1    Tong, Y.2    Shih-Hsien, Y.3
  • 18
    • 67650423968 scopus 로고    scopus 로고
    • Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions
    • Desvillettes Laurent, Mouhot Clément (2009) Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions. Arch Ration Mech An 193:227-253.
    • (2009) Arch Ration Mech An , vol.193 , pp. 227-253
    • Laurent, D.1    Clément, M.2
  • 19
    • 41849151052 scopus 로고    scopus 로고
    • On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity
    • Fournier Nicolas, Guérin Hélène (2008) On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity. J Stat Phys 131:749-781.
    • (2008) J Stat Phys , vol.131 , pp. 749-781
    • Nicolas, F.1    Hélène, G.2
  • 21
    • 0003840403 scopus 로고    scopus 로고
    • On the singularities of the global small solutions of the full Boltzmann equation
    • Boudin Laurent, Desvillettes Laurent (2000) On the singularities of the global small solutions of the full Boltzmann equation. Monatsh Math 131:91-108.
    • (2000) Monatsh Math , vol.131 , pp. 91-108
    • Laurent, B.1    Laurent, D.2
  • 22
    • 0001416655 scopus 로고
    • On Boltzmann and Landau equations
    • Lions P-L (1994) On Boltzmann and Landau equations. Philos Tr R Soc S-A 346:191-204.
    • (1994) Philos Tr R Soc S-A , vol.346 , pp. 191-204
    • Lions, P.-L.1
  • 23
    • 21844483733 scopus 로고
    • About the regularizing properties of the non-cut-off Kac equation
    • Desvillettes Laurent (1995) About the regularizing properties of the non-cut-off Kac equation. Commun Math Phys 168:417-440.
    • (1995) Commun Math Phys , vol.168 , pp. 417-440
    • Laurent, D.1
  • 24
    • 67349220644 scopus 로고    scopus 로고
    • Smoothing effects for classical solutions of the full Landau equation
    • Chen Yemin, Desvillettes Laurent, He Lingbing (2009) Smoothing effects for classical solutions of the full Landau equation. Arch Ration Mech An 193:21-55.
    • (2009) Arch Ration Mech An , vol.193 , pp. 21-55
    • Yemin, C.1    Laurent, D.2    Lingbing, H.3
  • 28
    • 34248226318 scopus 로고    scopus 로고
    • Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
    • arXiv:math.AP/0607495
    • Mouhot Clément, Strain Robert M (2007) Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff. J Math Pures Appl 87(5):515-535 (arXiv:math.AP/0607495).
    • (2007) J Math Pures Appl , vol.87 , Issue.5 , pp. 515-535
    • Clément, M.1    Strain Robert, M.2
  • 29
    • 0001964876 scopus 로고
    • Topics in harmonic analysis related to the Littlewood-Paley theory
    • Princeton Univ Press, Princeton, N.J
    • Stein EliasM(1970) Topics in harmonic analysis related to the Littlewood-Paley theory. Ann Math Stud (No.63, Princeton Univ Press, Princeton, N.J).
    • (1970) Ann Math Stud , Issue.63
    • Stein Elias, M.1
  • 30
    • 33646494047 scopus 로고    scopus 로고
    • A geometric approach to the Littlewood-Paley theory
    • Klainerman S, Rodnianski I (2006) A geometric approach to the Littlewood-Paley theory. Geom Funct Anal 16:126-163.
    • (2006) Geom Funct Anal , vol.16 , pp. 126-163
    • Klainerman, S.1    Rodnianski, I.2
  • 31
    • 0033240596 scopus 로고    scopus 로고
    • Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
    • Villani Cédric (1999) Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off. Rev Mat Iberoamericana 15:335-352.
    • (1999) Rev Mat Iberoamericana , vol.15 , pp. 335-352
    • Cédric, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.