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

Guo, Yan; Strauss, Walter A.

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, No. 3, 339-352 (1995).

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 \(v\).

MSC:

35Q35	PDEs in connection with fluid mechanics
76X05	Ionized gas flow in electromagnetic fields; plasmic flow

Keywords:

Vlasov-Poisson system; Penrose linear instability condition

References:

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