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A note on the nonlinear stability of a spatially symmetric Vlasov-Poisson flow. (English) Zbl 0609.35008
The Vlasov-Poisson equation was used to model a continuum of electrons moving in a \(\nu\)-dimensional flat torus. The Coulomb interaction was assumed for charged particles. The system is neutralized by a spatially uniform, positively charged background. The authors studied the problem of nonlinear stability of a special class of stationary solutions with respect to perturbations of the initial datum. Sufficient conditions were given for the homogeneous case with non-smooth solutions. This indicates that the constants appearing in the stability result do not depend on the regularity of the problem.
Reviewer: L.Shih

MSC:
35B35 Stability in context of PDEs
82D10 Statistical mechanical studies of plasmas
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q99 Partial differential equations of mathematical physics and other areas of application
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