Nonlinear instability of double-humped equilibria

Yan Guo; Walter A. Strauss

Annales de l'I.H.P. Analyse non linéaire (1995)

  • Volume: 12, Issue: 3, page 339-352
  • ISSN: 0294-1449

How to cite

top

Guo, Yan, and Strauss, Walter A.. "Nonlinear instability of double-humped equilibria." Annales de l'I.H.P. Analyse non linéaire 12.3 (1995): 339-352. <http://eudml.org/doc/78362>.

@article{Guo1995,
author = {Guo, Yan, Strauss, Walter A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Vlasov-Poisson system; Penrose linear instability condition},
language = {eng},
number = {3},
pages = {339-352},
publisher = {Gauthier-Villars},
title = {Nonlinear instability of double-humped equilibria},
url = {http://eudml.org/doc/78362},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Guo, Yan
AU - Strauss, Walter A.
TI - Nonlinear instability of double-humped equilibria
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 3
SP - 339
EP - 352
LA - eng
KW - Vlasov-Poisson system; Penrose linear instability condition
UR - http://eudml.org/doc/78362
ER -

References

top
  1. [BR1] J. Batt and G. Rein, Global classical solutions of the periodic Vlasov-Poisson system in three dimensions, C. R. Acad. Sci. Paris, t. 313, Serie 1, 1991, pp. 411-416. Zbl0741.35058MR1126425
  2. [BR2] J. Batt and G. Rein, A rigorous stability result for the Vlasov-Poisson equation in three dimensions, Anal. di Mat. Pura ed Appl., Vol. 164, 1993, pp. 133-154. Zbl0791.49030MR1243953
  3. [G] C.S. Gardner, Bound on the energy available from a plasma, Phys. Fluids, Vol. 6, 1963, pp. 839-840. MR152330
  4. [HM] D. Holm, J. Marsden, T. Ratiu and A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Phys. Rep., Vol. 123, 1985, pp. 1-116. Zbl0717.76051MR794110
  5. [H] E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Meth. Appl. Sci., Vol. 16, 1993, pp. 75-85. Zbl0782.35079MR1200156
  6. [GSS] M. Grillakis, J. Shatah and W. Strauss, Stability theory of solitary waves in the presence of symmetry, part 2, J. Funct. Anal., Vol. 94, 2, 1990, pp. 308-348. Zbl0711.58013MR1081647
  7. [K] N.A. Krall and A.W. Trivelpiece, Principles of Plasma Physics, McGraw-Hill, 1973. 
  8. [LP] P. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math., Vol. 105, 1991, pp. 415- 430. Zbl0741.35061MR1115549
  9. [MP] C. Marchioro and M. Pulvirenti, A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flow, Math. Mech. in the Appl. Sci., Vol. 8, 1986, pp. 284-288. Zbl0609.35008MR845931
  10. [P] O. Penrose, Electrostatic instability of a uniform non-Maxwellian plasma, Phys. Fluids, Vol. 3, 1960, pp. 258-265. Zbl0090.22801
  11. [Pf] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eqns., Vol. 92, 1992, pp. 281-303. Zbl0810.35089MR1165424
  12. [S] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. P.D.E., Vol. 16, 1991, pp. 1313-1335. Zbl0746.35050MR1132787
  13. [Sh] Y. Shizuta, On the classical solutions of the Boltzmann equation, Comm. Pure Appl. Math., Vol. 36, 1983, pp. 705-754. Zbl0515.35002MR720591

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.