메뉴 건너뛰기




Volumn 129, Issue 2, 2007, Pages 241-263

Quasi-stationary states for particle systems in the mean-field limit

Author keywords

Long time estimates; Metastability; N particle systems; Vlasov equation

Indexed keywords


EID: 35348909572     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9390-1     Document Type: Article
Times cited : (25)

References (27)
  • 1
    • 0001356905 scopus 로고
    • Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • 1
    • Arnold, V.: Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16(1), 319-361 (1966)
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , pp. 319-361
    • Arnold, V.1
  • 2
    • 21844524772 scopus 로고
    • Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
    • 2
    • Batt, J., Morrison, P.J., Rein, G.: Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions. Arch. Ration. Mech. Anal. 130(2), 163-182 (1995)
    • (1995) Arch. Ration. Mech. Anal. , vol.130 , pp. 163-182
    • Batt, J.1    Morrison, P.J.2    Rein, G.3
  • 3
    • 0001103153 scopus 로고
    • A rigorous stability result for the Vlasov-Poisson system in three dimensions
    • Batt, J., Rein, G.: A rigorous stability result for the Vlasov-Poisson system in three dimensions. Ann. Mat. Pure Appl. (4) 164, 133-154 (1993)
    • (1993) Ann. Mat. Pure Appl. (4) , vol.164 , pp. 133-154
    • Batt, J.1    Rein, G.2
  • 4
    • 42749098734 scopus 로고    scopus 로고
    • The stochastic process of equilibrium fluctuations, of a system with long range interactions
    • Bouchet, F.: The stochastic process of equilibrium fluctuations, of a system with long range interactions. Phys. Rev. E 70, 036113 (2004)
    • (2004) Phys. Rev. e , vol.70 , pp. 036113
    • Bouchet, F.1
  • 6
    • 0000009557 scopus 로고
    • The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles
    • 2
    • Braun, W., Hepp, K.: The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles. Commun. Math. Phys. 56(2), 101-113 (1977)
    • (1977) Commun. Math. Phys. , vol.56 , pp. 101-113
    • Braun, W.1    Hepp, K.2
  • 7
    • 2442717881 scopus 로고    scopus 로고
    • Stability of solutions of hydrodynamic equations describing the scaling limit of a massive piston in an ideal gas
    • Caglioti, E., Chernov, N., Lebowitz, J.: Stability of solutions of hydrodynamic equations describing the scaling limit of a massive piston in an ideal gas. Nonlinearity 17, 897-923 (2004)
    • (2004) Nonlinearity , vol.17 , pp. 897-923
    • Caglioti, E.1    Chernov, N.2    Lebowitz, J.3
  • 9
    • 4243748493 scopus 로고    scopus 로고
    • Kinetic theory of point vortices: Diffusion coefficient and systematic drift
    • Chavanis, P.H.: Kinetic theory of point vortices: diffusion coefficient and systematic drift. Phys. Rev. E 64, 026309 (2001)
    • (2001) Phys. Rev. e , vol.64 , pp. 026309
    • Chavanis, P.H.1
  • 10
    • 0036388126 scopus 로고    scopus 로고
    • Dynamics of a massive piston in an ideal gas: Oscillatory motion and approach to equilibrium
    • Chernov, N., Lebowitz, J.: Dynamics of a massive piston in an ideal gas: oscillatory motion and approach to equilibrium. J. Stat. Phys. 109, 507-527 (2002)
    • (2002) J. Stat. Phys. , vol.109 , pp. 507-527
    • Chernov, N.1    Lebowitz, J.2
  • 11
    • 0036390808 scopus 로고    scopus 로고
    • Scaling dynamic of a massive piston in a cube filled with ideal gas: Exact results
    • Chernov, N., Lebowitz, J., Sinai, Y.G.: Scaling dynamic of a massive piston in a cube filled with ideal gas: exact results. J. Stat. Phys. 109, 529-548 (2002)
    • (2002) J. Stat. Phys. , vol.109 , pp. 529-548
    • Chernov, N.1    Lebowitz, J.2    Sinai, Y.G.3
  • 12
    • 0037651092 scopus 로고    scopus 로고
    • Dynamics of a massive piston in an ideal gas
    • Chernov, N., Lebowitz, J., Sinai, Y.G.: Dynamics of a massive piston in an ideal gas. Russ. Math. Surv. 57, 1045-1125 (2002)
    • (2002) Russ. Math. Surv. , vol.57 , pp. 1045-1125
    • Chernov, N.1    Lebowitz, J.2    Sinai, Y.G.3
  • 14
    • 84990557431 scopus 로고
    • New stability estimates for the 2-D vortex method
    • 8-9
    • Goodman, J., Hou, T.Y.: New stability estimates for the 2-D vortex method. Commun. Pure Appl. Math. 44(8-9), 1015-1031 (1991)
    • (1991) Commun. Pure Appl. Math. , vol.44 , pp. 1015-1031
    • Goodman, J.1    Hou, T.Y.2
  • 15
    • 0038505911 scopus 로고    scopus 로고
    • Two times scale relaxation towards thermal equilibrium of the enigmatic piston
    • Gruber, C., Pache, S., Lesne, A.: Two times scale relaxation towards thermal equilibrium of the enigmatic piston. J. Stat. Phys. 112, 1199-1228 (2003)
    • (2003) J. Stat. Phys. , vol.112 , pp. 1199-1228
    • Gruber, C.1    Pache, S.2    Lesne, A.3
  • 16
    • 33846818719 scopus 로고    scopus 로고
    • N particles approximation of the Vlasov equations with singular potential
    • 3
    • Hauray, M., Jabin, P.-E.: N particles approximation of the Vlasov equations with singular potential. Arch. Ration. Mech. Anal. 183(3), 489-524 (2007)
    • (2007) Arch. Ration. Mech. Anal. , vol.183 , pp. 489-524
    • Hauray, M.1    Jabin, P.-E.2
  • 17
    • 0002245635 scopus 로고
    • Nonlinear stability of fluid and plasma equilibria
    • 1-2
    • Holm, D.D., Marsden, J.E., Ratiu, T., Weinstein, A.: Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123(1-2), 116 (1985)
    • (1985) Phys. Rep. , vol.123 , pp. 116
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3    Weinstein, A.4
  • 19
    • 0038995935 scopus 로고
    • Some considerations on the nonlinear stability of stationary planar Euler flows
    • 3
    • Marchioro, C., Pulvirenti, M.: Some considerations on the nonlinear stability of stationary planar Euler flows. Commun. Math. Phys. 100(3), 343-354 (1985)
    • (1985) Commun. Math. Phys. , vol.100 , pp. 343-354
    • Marchioro, C.1    Pulvirenti, M.2
  • 20
    • 0022579094 scopus 로고
    • A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flow
    • 2
    • Marchioro, C., Pulvirenti, M.: A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flow. Math. Methods Appl. Sci. 8(2), 284-288 (1986)
    • (1986) Math. Methods Appl. Sci. , vol.8 , pp. 284-288
    • Marchioro, C.1    Pulvirenti, M.2
  • 21
    • 0003394598 scopus 로고
    • Mathematical theory of incompressible nonviscous fluids
    • Springer New York
    • Marchioro, C., Pulvirenti, M.: Mathematical theory of incompressible nonviscous fluids. In: Applied Mathematical Sciences, vol. 96. Springer, New York (1994)
    • (1994) Applied Mathematical Sciences , vol.96
    • Marchioro, C.1    Pulvirenti, M.2
  • 22
    • 0010322607 scopus 로고
    • An introduction to the nonlinear Boltzmann-Vlasov equation
    • Kinetic Theories and the Boltzmann Equation (Montecatini, 1981). Springer Berlin
    • Neunzert, H.: An introduction to the nonlinear Boltzmann-Vlasov equation. In: Kinetic Theories and the Boltzmann Equation (Montecatini, 1981). Lecture Notes in Math., vol. 1048, pp. 60-110. Springer, Berlin (1984)
    • (1984) Lecture Notes in Math. , vol.1048 , pp. 60-110
    • Neunzert, H.1
  • 23
    • 0001550673 scopus 로고
    • Electrostatic instability of a uniform non-Maxwellian plasma
    • Penrose, O.: Electrostatic instability of a uniform non-Maxwellian plasma. Phys. Fluids 3, 258-265 (1960)
    • (1960) Phys. Fluids , vol.3 , pp. 258-265
    • Penrose, O.1
  • 24
    • 0028539404 scopus 로고
    • Non-linear stability for the Vlasov-Poisson system-the energy-Casimir method
    • 14
    • Rein, G.: Non-linear stability for the Vlasov-Poisson system-the energy-Casimir method. Math. Methods Appl. Sci. 17(14), 1129-1140 (1994)
    • (1994) Math. Methods Appl. Sci. , vol.17 , pp. 1129-1140
    • Rein, G.1
  • 27
    • 1842563884 scopus 로고    scopus 로고
    • Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
    • Yamaguchi, Y.Y., Barré, J., Bouchet, F., Dauxois, T., Ruffo, S.: Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model. Physica A 337, 36-66 (2004)
    • (2004) Physica A , vol.337 , pp. 36-66
    • Yamaguchi, Y.Y.1    Barré, J.2    Bouchet, F.3    Dauxois, T.4    Ruffo, S.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.