Stability for the gravitational Vlasov-Poisson system in dimension two

被引：4
作者：
Dolbeault, J.
Fernandez, J.
Sanchez, O.
机构：
[1] Univ Paris 09, UMR 7534, CNRS, F-75775 Paris 16, France
[2] Univ Granada, Dept Matemat Aplicada, Fac Ciencias, E-18071 Granada, Spain
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 31卷 / 10期
关键词：
bounded solutions; direct variational methods; Dirichlet boundary conditions; dynamical stability; energy; gravitation; Hardy-Littlewood-Sobolev inequality; interpolation; kinetic energy; Lagrange multiplier; mass; minimization; minimizers; optimal constants; polytropic gas spheres; potential energy; Riesz theorem; scalings; semilinear elliptic equations; solutions with compact support; Stellar dynamics; symmetric nonincreasing rearrangements; uniqueness; Vlasov-Poisson system;
D O I：
10.1080/03605300500481517
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the two dimensional gravitational Vlasov-Poisson system. Using variational methods, we prove the existence of stationary solutions of minimal energy under a Casimir type constraint. The method also provides a stability criterion of these solutions for the evolution problem.
引用
收藏
页码：1425 / 1449
页数：25
相关论文
共 22 条
[1]   STATIONARY SPHERICALLY SYMMETRICAL MODELS IN STELLAR DYNAMICS [J].
BATT, J ;
FALTENBACHER, W ;
HORST, E .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1986, 93 (02) :159-183
[2]  
Binney J., 2008, Galactic dynamics, V2nd ed.
[3]   A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].
BREZIS, H ;
LIEB, E .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490
[4]   Nonlinear stability in Lp for a confined system of charged particles [J].
Cáceres, MJ ;
Carrillo, JA ;
Dolbeault, J .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2002, 34 (02) :478-494
[5]  
CARLEN E., 1992, Geom. Funct. Anal., V2, P90, DOI [DOI 10.1007/BF01895706, 10.1007/BF01895706]
[6]  
Dautray R., 1988, MATH ANAL NUMERICAL, V2
[7]   Monokinetic charged particle beams:: Qualitative behavior of the solutions of the cauchy problem and 2d time-periodic solutions of the Vlasov-Poisson system [J].
Dolbeault, J .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (9-10) :1567-1647
[8]   Asymptotic behaviour for the Vlasov-Poisson system in the stellar-dynamics case [J].
Dolbeault, J ;
Sánchez, O ;
Soler, J .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2004, 171 (03) :301-327
[9]  
GERARD P, 1989, SOLUTIONS GLOBALES P, P257
[10]   SYMMETRY AND RELATED PROPERTIES VIA THE MAXIMUM PRINCIPLE [J].
GIDAS, B ;
NI, WM ;
NIRENBERG, L .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 68 (03) :209-243
123