Anisotropie dans un plasma fortement magnétisé

Daniel Han-Kwan[1]

  • [1] DMA, École Normale Supérieure 45 rue d’Ulm 75005 Paris France

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • page 1-14
  • ISSN: 2266-0607

Abstract

top
Nous présentons les résultats prouvés dans [20, 22], qui concernent l’étude asymptotique de l’équation de Vlasov-Poisson dans un régime quasineutre et de champ magnétique intense. Nous insisterons en particulier sur les conséquences de l’anisotropie du problème physique sur l’analyse mathématique.

How to cite

top

Han-Kwan, Daniel. "Anisotropie dans un plasma fortement magnétisé." Séminaire Laurent Schwartz — EDP et applications (2011-2012): 1-14. <http://eudml.org/doc/251164>.

@article{Han2011-2012,
abstract = {Nous présentons les résultats prouvés dans [20, 22], qui concernent l’étude asymptotique de l’équation de Vlasov-Poisson dans un régime quasineutre et de champ magnétique intense. Nous insisterons en particulier sur les conséquences de l’anisotropie du problème physique sur l’analyse mathématique.},
affiliation = {DMA, École Normale Supérieure 45 rue d’Ulm 75005 Paris France},
author = {Han-Kwan, Daniel},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {fre},
pages = {1-14},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Anisotropie dans un plasma fortement magnétisé},
url = {http://eudml.org/doc/251164},
year = {2011-2012},
}

TY - JOUR
AU - Han-Kwan, Daniel
TI - Anisotropie dans un plasma fortement magnétisé
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 14
AB - Nous présentons les résultats prouvés dans [20, 22], qui concernent l’étude asymptotique de l’équation de Vlasov-Poisson dans un régime quasineutre et de champ magnétique intense. Nous insisterons en particulier sur les conséquences de l’anisotropie du problème physique sur l’analyse mathématique.
LA - fre
UR - http://eudml.org/doc/251164
ER -

References

top
  1. G. Allaire. Homogenization and two-scale convergence. SIAM J. Math. Anal., 23(6) :1482–1518, 1992. Zbl0770.35005MR1185639
  2. M. Bostan. The Vlasov-Poisson system with strong external magnetic field. Finite Larmor radius regime. Asymptot. Anal., 61(2) :91–123, 2009. Zbl1180.35501MR2499194
  3. Y. Brenier. A homogenized model for vortex sheets. Arch. Rational Mech. Anal., 138(4) :319–353, 1997. Zbl0962.35140MR1467558
  4. Y. Brenier. Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations, 25(3-4) :737–754, 2000. Zbl0970.35110MR1748352
  5. Y. Brenier and E. Grenier. Limite singulière du système de Vlasov-Poisson dans le régime de quasi neutralité : le cas indépendant du temps. C. R. Acad. Sci. Paris Sér. I Math., 318(2) :121–124, 1994. Zbl0803.35110MR1260322
  6. S. Cordier, E. Grenier, and Y. Guo. Two-stream instabilities in plasmas. Methods Appl. Anal., 7(2) :391–405, 2000. Cathleen Morawetz : a great mathematician. Zbl1002.82029MR1869291
  7. R. J. DiPerna and P.-L. Lions. Global weak solutions of Vlasov-Maxwell systems. Comm. Pure Appl. Math., 42(6) :729–757, 1989. Zbl0698.35128MR1003433
  8. R. J. DiPerna, P.-L. Lions, and Y. Meyer. L p regularity of velocity averages. Ann. Inst. H. Poincaré Anal. Non Linéaire, 8(3-4) :271–287, 1991. Zbl0763.35014MR1127927
  9. E. Frénod and A. Mouton. Two-dimensional finite Larmor radius approximation in canonical gyrokinetic coordinates. J. Pure Appl. Math. Adv. Appl., 4(2) :135–169, 2010. Zbl1225.35016MR2816864
  10. E. Frénod and E. Sonnendrücker. The finite Larmor radius approximation. SIAM J. Math. Anal., 32(6) :1227–1247 (electronic), 2001. Zbl0980.82030MR1856246
  11. P. Ghendrih, M. Hauray, and A. Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions. Kinet. and Relat. Models, 2(4) :707–725, 2009. Zbl1195.82087MR2556718
  12. F. Golse, P.L. Lions, B. Perthame, and R. Sentis. Regularity of the moments of the solution of a transport equation. J. Funct. Anal., 76(1) :110–125, 1988. Zbl0652.47031MR923047
  13. F. Golse and L. Saint-Raymond. The Vlasov-Poisson system with strong magnetic field. J. Math. Pures Appl. (9), 78(8) :791–817, 1999. Zbl0977.35108MR1715342
  14. F. Golse and L. Saint-Raymond. The Vlasov-Poisson system with strong magnetic field in quasineutral regime. Math. Models Methods Appl. Sci., 13(5) :661–714, 2003. Zbl1053.82032MR1978931
  15. V. Grandgirard et al. Global full- f gyrokinetic simulations of plasma turbulence. Plasma Phys. Control. Fusion, 49 :173–182, 2007. 
  16. E. Grenier. Defect measures of the Vlasov-Poisson system in the quasineutral regime. Comm. Partial Differential Equations, 20(7-8) :1189–1215, 1995. Zbl0828.35106MR1335748
  17. E. Grenier. Oscillations in quasineutral plasmas. Comm. Partial Differential Equations, 21(3-4) :363–394, 1996. Zbl0849.35107MR1387452
  18. E. Grenier. Limite quasineutre en dimension 1. In Journées “Équations aux Dérivées Partielles” (Saint-Jean-de-Monts, 1999), pages Exp. No. II, 8. Univ. Nantes, Nantes, 1999. Zbl1008.35054MR1718954
  19. Y. Guo and W. A. Strauss. Nonlinear instability of double-humped equilibria. Ann. Inst. H. Poincaré Anal. Non Linéaire, 12(3) :339–352, 1995. Zbl0836.35130MR1340268
  20. D. Han-Kwan. The three-dimensional finite Larmor radius approximation. Asymptot. Anal., 66(1) :9–33, 2010. Zbl1191.35267MR2582446
  21. D. Han-Kwan. Effect of the polarization drift in a strongly magnetized plasma. ESAIM Math. Mod. Num. Anal., 46(4) :929-947, 2012. Zbl1310.76190MR2891475
  22. D. Han-Kwan. On the three-dimensional finite Larmor radius approximation : the case of electrons in a fixed background of ions. Soumis, 2011. Zbl1191.35267MR2582446
  23. D. Han-Kwan. Quasineutral limit of the Vlasov-Poisson system with massless electrons. Comm. Partial Differential Equations, 36(8) :1385–1425, 2011. Zbl1228.35251MR2825596
  24. M. Hauray and A. Nouri. Well-posedness of a diffusive gyro-kinetic model. To appear in Ann. IHP (Analyse Non Linéaire), 2011. Zbl1269.82075MR2823883
  25. P.-E. Jabin. Averaging lemmas and dispersion estimates for kinetic equations. Riv. Mat. Univ. Parma (8), 1 :71–138, 2009. Zbl1190.35152MR2597793
  26. G. Loeper. Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. Comm. Partial Differential Equations, 30(7-9) :1141–1167, 2005. Zbl1077.76072MR2180297
  27. N. Masmoudi. From Vlasov-Poisson system to the incompressible Euler system. Comm. Partial Differential Equations, 26(9) :1913–1928, 2001. Zbl1083.35116MR1865949
  28. C. Mouhot and C. Villani. On Landau damping. To appear in Acta Mathematica, 2011. Zbl1239.82017MR2863910
  29. G. Nguetseng. A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal., 20(3) :608–623, 1989. Zbl0688.35007MR990867
  30. L. Nirenberg. An abstract form of the nonlinear Cauchy-Kowalewski theorem. J. Differential Geom., 6 :561–576, 1972. Zbl0257.35001MR322321
  31. T. Nishida. A note on a theorem of Nirenbeg. J. Differential Geom., 12 :629–633, 1977. Zbl0368.35007MR512931
  32. O. Penrose. Electrostatic instability of a uniform non-Maxwellian plasma. Phys. Fluids, 3 :258–265, 1960. Zbl0090.22801

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.