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Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain
Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system
1. | Department of Mathematics, Indiana University, Bloomington, IN 47405 |
2. | Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80002 |
3. | Department of Mathematics Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 |
References:
[1] |
R. J. DiPerna and P. L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[2] |
R. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[3] |
R. Glassey, S. Pankavich and J. Schaeffer, Large time behavior of the relativistic vlasov-maxwell system in low space dimension, Differential and Integral Equations, 23 (2010), 61-77. |
[4] |
R. Glassey, S. Pankavich and J. Schaeffer, Long-time behavior of monocharged and neutral plasmas in "One and one-half" dimensions, Kinetic and Related Models, 2 (2009), 465-488.
doi: 10.3934/krm.2009.2.465. |
[5] |
R. Glassey, S. Pankavich and J. Schaeffer, Decay in time for a one-dimensional, two component plasma, Math. Meth. Appl. Sci., 31 (2008), 2115-2132.
doi: 10.1002/mma.1015. |
[6] |
R. Glassey and J. Schaeffer, On the "one and one-half dimensional'' relativistic Vlasov-Maxwell system, Math. Methods Appl. Sci., 13 (1990), 169-179.
doi: 10.1002/mma.1670130207. |
[7] |
R. Glassey and J. Schaeffer, The "two and one-half-dimensional'' relativistic Vlasov Maxwell system, Comm. Math. Phys., 185 (1997), 257-284.
doi: 10.1007/s002200050090. |
[8] |
R. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions I, Arch. Rational Mech. Anal., 141 (1998), 331-354.
doi: 10.1007/s002050050079. |
[9] |
R. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions II, Arch. Rational Mech. Anal., 141 (1998), 355-374.
doi: 10.1007/s002050050079. |
[10] |
R. Glassey and W. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[11] |
R. Glassey and W. Strauss, Remarks on collisionless plasmas, Fluids and plasmas: geometry and dynamics, (Boulder, CO., 1983), Contemp. Math., Amer. Math. Soc., Providence, RI, 28 (1984), 269-279.
doi: 10.1090/conm/028/751989. |
[12] |
P. Lions and P. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[13] |
S. Pankavich and C. Nguyen, A one-dimensional kinetic model of plasma dynamics with a transport field, Evolution Equations and Control Theory, 3 (2014), 681-698.
doi: 10.3934/eect.2014.3.681. |
[14] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Equations, 95 (1992), 281-303.
doi: 10.1016/0022-0396(92)90033-J. |
[15] |
J. Schaeffer, Global existence of smooth solutions to the vlasov-poisson system in three dimensions, Commun. PDE, 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[16] |
N. G. van Kampen and B. U. Felderhof, Theoretical Methods in Plasma Physics, Wiley: New York, NY, 1967. |
show all references
References:
[1] |
R. J. DiPerna and P. L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[2] |
R. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[3] |
R. Glassey, S. Pankavich and J. Schaeffer, Large time behavior of the relativistic vlasov-maxwell system in low space dimension, Differential and Integral Equations, 23 (2010), 61-77. |
[4] |
R. Glassey, S. Pankavich and J. Schaeffer, Long-time behavior of monocharged and neutral plasmas in "One and one-half" dimensions, Kinetic and Related Models, 2 (2009), 465-488.
doi: 10.3934/krm.2009.2.465. |
[5] |
R. Glassey, S. Pankavich and J. Schaeffer, Decay in time for a one-dimensional, two component plasma, Math. Meth. Appl. Sci., 31 (2008), 2115-2132.
doi: 10.1002/mma.1015. |
[6] |
R. Glassey and J. Schaeffer, On the "one and one-half dimensional'' relativistic Vlasov-Maxwell system, Math. Methods Appl. Sci., 13 (1990), 169-179.
doi: 10.1002/mma.1670130207. |
[7] |
R. Glassey and J. Schaeffer, The "two and one-half-dimensional'' relativistic Vlasov Maxwell system, Comm. Math. Phys., 185 (1997), 257-284.
doi: 10.1007/s002200050090. |
[8] |
R. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions I, Arch. Rational Mech. Anal., 141 (1998), 331-354.
doi: 10.1007/s002050050079. |
[9] |
R. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions II, Arch. Rational Mech. Anal., 141 (1998), 355-374.
doi: 10.1007/s002050050079. |
[10] |
R. Glassey and W. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[11] |
R. Glassey and W. Strauss, Remarks on collisionless plasmas, Fluids and plasmas: geometry and dynamics, (Boulder, CO., 1983), Contemp. Math., Amer. Math. Soc., Providence, RI, 28 (1984), 269-279.
doi: 10.1090/conm/028/751989. |
[12] |
P. Lions and P. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[13] |
S. Pankavich and C. Nguyen, A one-dimensional kinetic model of plasma dynamics with a transport field, Evolution Equations and Control Theory, 3 (2014), 681-698.
doi: 10.3934/eect.2014.3.681. |
[14] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Equations, 95 (1992), 281-303.
doi: 10.1016/0022-0396(92)90033-J. |
[15] |
J. Schaeffer, Global existence of smooth solutions to the vlasov-poisson system in three dimensions, Commun. PDE, 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[16] |
N. G. van Kampen and B. U. Felderhof, Theoretical Methods in Plasma Physics, Wiley: New York, NY, 1967. |
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