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Volumn 37, Issue 6, 2006, Pages 1709-1731

New lyapunov functionals of the Vlasov-poisson system

Author keywords

Instability; Lyapunov functional; Vlasov Poisson system

Indexed keywords

ELECTRIC FIELDS; FUNCTION EVALUATION; LYAPUNOV METHODS; PHASE SPACE METHODS; STABILITY; TRAJECTORIES;

EID: 33747709341     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/040621338     Document Type: Article
Times cited : (14)

References (40)
  • 1
    • 49649145288 scopus 로고
    • Global existence of a weak solution of Vlasov's system of equations
    • A. A. ARSENEV, Global existence of a weak solution of Vlasov's system of equations, U.S.S.R. Comput. Math. Math. Phys., 15 (1975), pp. 131-143.
    • (1975) U.S.S.R. Comput. Math. Math. Phys. , vol.15 , pp. 131-143
    • Arsenev, A.A.1
  • 2
    • 65449177851 scopus 로고
    • Global existence for the Vlasov-Poisson equation in three space variables with small initial data
    • C. BARDOS AND P. DEGOND, Global existence for the Vlasov-Poisson equation in three space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), pp. 101-118.
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , pp. 101-118
    • Bardos, C.1    Degond, P.2
  • 3
    • 0000037275 scopus 로고
    • Global symmetric solutions of the initial value problem of stellar dynamic
    • J. BATT, Global symmetric solutions of the initial value problem of stellar dynamic, J. Differential Equations, 25 (1977), pp. 342-364.
    • (1977) J. Differential Equations , vol.25 , pp. 342-364
    • Batt, J.1
  • 4
    • 0001103153 scopus 로고
    • A rigorous stability result for the Vlasov-Poisson system in three dimensions
    • J. BATT AND R. REIN, A rigorous stability result for the Vlasov-Poisson system in three dimensions, Anal. Mat. Pura Appl., 164 (1993), pp. 133-154.
    • (1993) Anal. Mat. Pura Appl. , vol.164 , pp. 133-154
    • Batt, J.1    Rein, R.2
  • 5
    • 0242370972 scopus 로고    scopus 로고
    • Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system
    • F. BOUCHUT, F. GOLSE, AND C. PALLARD, Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system, Arch. Ration. Mech. Anal., 170 (2003), pp. 1-15.
    • (2003) Arch. Ration. Mech. Anal. , vol.170 , pp. 1-15
    • Bouchut, F.1    Golse, F.2    Pallard, C.3
  • 8
    • 0032381779 scopus 로고    scopus 로고
    • The relativistic Vlasov-Maxwell system in two space dimensions: Part I
    • R. GLASSEY AND J. SCHAEFFER, The relativistic Vlasov-Maxwell system in two space dimensions: Part I, Arch. Ration. Mech. Anal., 141 (1998), pp. 331-354.
    • (1998) Arch. Ration. Mech. Anal. , vol.141 , pp. 331-354
    • Glassey, R.1    Schaeffer, J.2
  • 9
    • 0032366147 scopus 로고    scopus 로고
    • The relativistic Vlasov-Maxwell system in two space dimensions: Part II
    • R. GLASSEY AND J. SCHAEFFER, The relativistic Vlasov-Maxwell system in two space dimensions: Part II, Arch. Ration. Mech. Anal., 141 (1998), pp. 355-374.
    • (1998) Arch. Ration. Mech. Anal. , vol.141 , pp. 355-374
    • Glassey, R.1    Schaeffer, J.2
  • 10
    • 0031138746 scopus 로고    scopus 로고
    • The two and one-half dimensional relativistic Vlasov-Maxwell system
    • R. GLASSEY AND J. SCHAEFFER, The two and one-half dimensional relativistic Vlasov-Maxwell system, Comm. Math. Phys., 185 (1997), pp. 257-284.
    • (1997) Comm. Math. Phys. , vol.185 , pp. 257-284
    • Glassey, R.1    Schaeffer, J.2
  • 11
    • 0001870782 scopus 로고
    • Global existence of the relativistic Vlasov-Maxwell system with nearly neutral initial data
    • R. GLASSEY AND J. SCHAEFFER, Global existence of the relativistic Vlasov-Maxwell system with nearly neutral initial data, Comm. Math. Phys., 119 (1988), pp. 353-384.
    • (1988) Comm. Math. Phys. , vol.119 , pp. 353-384
    • Glassey, R.1    Schaeffer, J.2
  • 12
    • 0037484826 scopus 로고
    • On symmetric solutions to the relativistic Vlasov-Poisson system
    • R. GLASSEY AND J. SCHAEFFER, On symmetric solutions to the relativistic Vlasov-Poisson system, Comm. Math. Phys., 101 (1985), pp. 459-473.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 459-473
    • Glassey, R.1    Schaeffer, J.2
  • 13
    • 0013373668 scopus 로고
    • Large velocities in the relativistic Vlasov-Maxwell equations
    • R. GLASSEY AND W. STRAUSS, Large velocities in the relativistic Vlasov-Maxwell equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 36 (1989), pp. 615-627.
    • (1989) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.36 , pp. 615-627
    • Glassey, R.1    Strauss, W.2
  • 14
    • 0023210259 scopus 로고
    • High velocity particles in a collisionless plasma
    • R. GLASSEY AND W. STRAUSS, High velocity particles in a collisionless plasma, Math. Mech. Appl. Sci., 9 (1987), pp. 45-52.
    • (1987) Math. Mech. Appl. Sci. , vol.9 , pp. 45-52
    • Glassey, R.1    Strauss, W.2
  • 15
    • 0001882025 scopus 로고
    • Absence of shocks in an initially dilute collisionless plasma
    • R. GLASSEY AND W. STRAUSS, Absence of shocks in an initially dilute collisionless plasma, Comm. Math. Phys., 113 (1987), pp. 191-208.
    • (1987) Comm. Math. Phys. , vol.113 , pp. 191-208
    • Glassey, R.1    Strauss, W.2
  • 16
    • 34250124626 scopus 로고
    • Singularity formation in a collisionless plasma could occur only at high velocities
    • R. GLASSEY AND W. STRAUSS, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Ration. Mech. Anal., 92 (1986), pp. 59-90.
    • (1986) Arch. Ration. Mech. Anal. , vol.92 , pp. 59-90
    • Glassey, R.1    Strauss, W.2
  • 17
    • 84981759861 scopus 로고
    • Solutions in the large for nonlinear hyperbolic systems of equations
    • J. GLIMM, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), pp. 697-715.
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 697-715
    • Glimm, J.1
  • 18
    • 0035531905 scopus 로고    scopus 로고
    • The Vlasov-Poisson-Boltzmann system near vacuum
    • Y. GUO, The Vlasov-Poisson-Boltzmann system near vacuum, Comm. Math. Phys., 218 (2001), pp. 293-313.
    • (2001) Comm. Math. Phys. , vol.218 , pp. 293-313
    • Guo, Y.1
  • 19
    • 4344614225 scopus 로고    scopus 로고
    • 1-stability of the Boltzmann equation for the hard sphere model
    • 1-stability of the Boltzmann equation for the hard sphere model, Arch. Ration. Mech. Anal., 173 (2004), pp. 279-296.
    • (2004) Arch. Ration. Mech. Anal. , vol.173 , pp. 279-296
    • Ha, S.Y.1
  • 20
    • 18144375596 scopus 로고    scopus 로고
    • Stability estimates of the Boltzmann equation and uniform stability estimates
    • S. Y. HA, Stability estimates of the Boltzmann equation and uniform stability estimates, J. Differential Equations, 215 (2005), pp. 178-205.
    • (2005) J. Differential Equations , vol.215 , pp. 178-205
    • Ha, S.Y.1
  • 21
    • 0019655802 scopus 로고
    • On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation (Part I)
    • E. HORST, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation (Part I), Math. Methods Appl. Sci., 3 (1981), pp. 229-248.
    • (1981) Math. Methods Appl. Sci. , vol.3 , pp. 229-248
    • Horst, E.1
  • 22
    • 0002923971 scopus 로고
    • On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation (Part II)
    • E. HORST, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation (Part II), Math. Methods Appl. Sci., 4 (1982), pp. 19-32.
    • (1982) Math. Methods Appl. Sci. , vol.4 , pp. 19-32
    • Horst, E.1
  • 23
    • 0003107088 scopus 로고
    • On the asymptotic growth of the solutions of the Vlasov-Poisson system
    • E. HORST, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Methods Appl. Sci., 16 (1993), pp. 75-85.
    • (1993) Math. Methods Appl. Sci. , vol.16 , pp. 75-85
    • Horst, E.1
  • 24
    • 0021303282 scopus 로고
    • Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation
    • E. HORST AND R. HUNZE, Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Math. Methods Appl. Sci., 6 (1984), pp. 262-279.
    • (1984) Math. Methods Appl. Sci. , vol.6 , pp. 262-279
    • Horst, E.1    Hunze, R.2
  • 25
    • 0000652131 scopus 로고
    • The Cauchy problem for the kinetic equation of plasma
    • S. V. IORDANSKII, The Cauchy problem for the kinetic equation of plasma, Amer. Math. Soc. Transl. Ser., 35 (1964), pp. 351-363.
    • (1964) Amer. Math. Soc. Transl. Ser. , vol.35 , pp. 351-363
    • Iordanskii, S.V.1
  • 26
    • 0038396619 scopus 로고    scopus 로고
    • A new approach to study the Vlasov-Maxwell system
    • S. KLAINERMAN AND G. STAFFILANI, A new approach to study the Vlasov-Maxwell system, Comm. Pure Appl. Anal., 1 (2002), pp. 103-125.
    • (2002) Comm. Pure Appl. Anal. , vol.1 , pp. 103-125
    • Klainerman, S.1    Staffilani, G.2
  • 27
    • 0001515315 scopus 로고
    • Propagation of moments and regularity of solutions for the 3-dimensional Vlasov-Poisson system
    • P. L. LIONS AND B. PERTHAME, Propagation of moments and regularity of solutions for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), pp. 415-430.
    • (1991) Invent. Math. , vol.105 , pp. 415-430
    • Lions, P.L.1    Perthame, B.2
  • 28
    • 2142694481 scopus 로고    scopus 로고
    • Mathematical tools for kinetic equations
    • N.S.
    • B. PERTHAME, Mathematical tools for kinetic equations, Bull. Amer. Math. Soc. (N.S.), 41 (2004), pp. 205-244.
    • (2004) Bull. Amer. Math. Soc. , vol.41 , pp. 205-244
    • Perthame, B.1
  • 29
    • 0002288656 scopus 로고    scopus 로고
    • Time decay, propagation of low moments and dispersive effects for kinetic equations
    • B. PERTHAME, Time decay, propagation of low moments and dispersive effects for kinetic equations, Comm. Partial Differential Equations, 21 (1996), pp. 659-686.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 659-686
    • Perthame, B.1
  • 30
    • 44049119012 scopus 로고
    • Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
    • K. PFAFFELMOSER, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Equations, 95 (1992), pp. 281-303.
    • (1992) J. Differential Equations , vol.95 , pp. 281-303
    • Pfaffelmoser, K.1
  • 31
    • 0028539404 scopus 로고
    • Nonlinear stability for the Vlasov-Poisson system-the energy Casimir method
    • G. REIN, Nonlinear stability for the Vlasov-Poisson system-the energy Casimir method, Math. Methods Appl. Sci., 17 (1994), pp. 1129-1140.
    • (1994) Math. Methods Appl. Sci. , vol.17 , pp. 1129-1140
    • Rein, G.1
  • 32
    • 2142830927 scopus 로고    scopus 로고
    • A small data theorem for collisionless plasma that includes high velocity particles
    • J. SCHAEFFER, A small data theorem for collisionless plasma that includes high velocity particles, Indiana Univ. Math. J., 53 (2004), pp. 1-34.
    • (2004) Indiana Univ. Math. J. , vol.53 , pp. 1-34
    • Schaeffer, J.1
  • 33
    • 0001072016 scopus 로고
    • Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions
    • J. SCHAEFFER, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Partial Differential Equations, 16 (1991), pp. 1313-1335.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 1313-1335
    • Schaeffer, J.1
  • 34
    • 0040533651 scopus 로고
    • Global existence for the Poisson-Vlasov system with nearly symmetric data
    • J. SCHAEFFER, Global existence for the Poisson-Vlasov system with nearly symmetric data, J. Differential Equations, 69 (1987), pp. 111-148.
    • (1987) J. Differential Equations , vol.69 , pp. 111-148
    • Schaeffer, J.1
  • 35
    • 0007465324 scopus 로고
    • The classical limit of the relativistic Vlasov-Maxwell system
    • J. SCHAEFFER, The classical limit of the relativistic Vlasov-Maxwell system, Comm. Math. Phys., 104 (1986), pp. 403-421.
    • (1986) Comm. Math. Phys. , vol.104 , pp. 403-421
    • Schaeffer, J.1
  • 36
    • 84972582450 scopus 로고
    • On classical solutions in the large in time of two-dimensional Vlasov's equation
    • S. UKAI AND T. OKABE, On classical solutions in the large in time of two-dimensional Vlasov's equation, Osaka J. Math., 15 (1978), pp. 245-261.
    • (1978) Osaka J. Math. , vol.15 , pp. 245-261
    • Ukai, S.1    Okabe, T.2
  • 37
    • 1542505365 scopus 로고
    • A discrete approximation to the one-dimensional Vlasov-Poisson system
    • S. WOLLMAN, A discrete approximation to the one-dimensional Vlasov-Poisson system, Transport Theory Statist. Phys., 17 (1988), pp. 561-594.
    • (1988) Transport Theory Statist. Phys. , vol.17 , pp. 561-594
    • Wollman, S.1
  • 38
    • 84980134145 scopus 로고
    • Global-in-time solutions to the two-dimensional Vlasov-Poisson system
    • S. WOLLMAN, Global-in-time solutions to the two-dimensional Vlasov-Poisson system, Comm. Pure Appl. Math., 33 (1980), pp. 173-197.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 173-197
    • Wollman, S.1
  • 39
    • 1542715026 scopus 로고
    • Convergence of a numerical approximation to the one dimensional Vlasov Poisson system
    • S. WOLLMAN, Convergence of a numerical approximation to the one dimensional Vlasov Poisson system, Transport Theory Statist. Phys., 19 (1990), pp. 545-562.
    • (1990) Transport Theory Statist. Phys. , vol.19 , pp. 545-562
    • Wollman, S.1
  • 40
    • 38249003691 scopus 로고
    • Global-in-time solutions to the three-dimensional Vlasov-Poisson system
    • S. WOLLMAN, Global-in-time solutions to the three-dimensional Vlasov-Poisson system, J. Math. Anal. Appl., 176 (1993), pp. 76-91.
    • (1993) J. Math. Anal. Appl. , vol.176 , pp. 76-91
    • Wollman, S.1


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