Stability for the gravitational Vlasov-Poisson system in dimension two
نویسندگان
چکیده
We consider the two dimensional gravitational VlasovPoisson 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. Key-words. Vlasov-Poisson system – stellar dynamics – polytropic gas spheres – gravitation – mass – energy – kinetic energy – potential energy – interpolation – Hardy-Littlewood-Sobolev inequality – optimal constants – symmetric nonincreasing rearrangements – Riesz’ theorem – bounded solutions – direct variational methods – minimization – scalings – solutions with compact support – minimizers – Lagrange multiplier – Semilinear elliptic equations – Uniqueness – Dirichlet boundary conditions – dynamical stability AMS classification (2000). Primary: 35A15, 82B40, 82C40; Secondary: 34A12, 35A05, 35B35, 35B40, 35B45, 35J05, 35J20, 35J25, 35J60, 76P05, 82D99
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