[Stabilité orbitale et formation de singularité pour des systèmes de Vlasov–Poisson]
Nous considérons le système de Vlasov–Poisson gravitationnel en dimensions
We study the gravitational Vlasov–Poisson system in dimension
Accepté le :
Publié le :
Mohammed Lemou 1 ; Florian Méhats 1 ; Pierre Raphael 2
@article{CRMATH_2005__341_4_269_0, author = {Mohammed Lemou and Florian M\'ehats and Pierre Raphael}, title = {Orbital stability and singularity formation for {Vlasov{\textendash}Poisson} systems}, journal = {Comptes Rendus. Math\'ematique}, pages = {269--274}, publisher = {Elsevier}, volume = {341}, number = {4}, year = {2005}, doi = {10.1016/j.crma.2005.06.018}, language = {en}, }
TY - JOUR AU - Mohammed Lemou AU - Florian Méhats AU - Pierre Raphael TI - Orbital stability and singularity formation for Vlasov–Poisson systems JO - Comptes Rendus. Mathématique PY - 2005 SP - 269 EP - 274 VL - 341 IS - 4 PB - Elsevier DO - 10.1016/j.crma.2005.06.018 LA - en ID - CRMATH_2005__341_4_269_0 ER -
Mohammed Lemou; Florian Méhats; Pierre Raphael. Orbital stability and singularity formation for Vlasov–Poisson systems. Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 269-274. doi : 10.1016/j.crma.2005.06.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.018/
[1] Kinetic Equations and Asymptotic Theory, Ser. Appl. Math., Gauthiers-Villars, Paris, 2000
[2] Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys., Volume 85 (1982) no. 4, pp. 549-561
[3] Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions, Phys. Rev. E, Volume 69 (2004), p. 066126
[4] Asymptotic behaviour for the Vlasov–Poisson system in the stellar-dynamics case, Arch. Rational Mech. Anal., Volume 171 (2004) no. 3, pp. 301-327
[5] The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996
[6] Variational method for stable polytropic galaxies, Arch. Rational Mech. Anal., Volume 130 (1995), pp. 163-182
[7] Isotropic steady states in galactic dynamics, Commun. Math. Phys., Volume 219 (2001), pp. 607-629
[8] Weak solutions of the initial value problem for the unmodified non-linear Vlasov equation, Math. Methods Appl. Sci., Volume 6 (1984), pp. 262-279
[9] M. Lemou, F. Méhats, P. Raphael, On the orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system, submitted for publication
[10] The concentration-compactness principle in the calculus of variations. The locally compact case, I. Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 1 (1984) no. 2, pp. 109-145
[11] Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation, Ann. of Math., Volume 161 (2005) no. 1, pp. 157-222
[12] Profiles and quantization of the blow up mass for critical non linear Schrödinger equation, Commun. Math. Phys., Volume 253 (2004) no. 3, pp. 675-704
[13]
[14] Ó. Sánchez, J. Soler, Orbital stability for polytropic galaxies, Preprint
[15] Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys., Volume 87 (1983), pp. 567-576
Cité par Sources :
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier