Nonlinear instability of double-humped equilibria. (English) Zbl 0836.35130

Summary: Consider a plasma described by the Vlasov-Poisson system in a cube \(Q\) with the specular boundary condition. We prove that an equilibrium \(\mu (v)\), which satisfies the Penrose linear instability condition and which decays like \(O (|v |^{-3})\), is nonlinearly unstable in the \(C^1\) norm with a weight function in \(v\).


35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
Full Text: DOI Numdam EuDML


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