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| We consider the homogeneous equilibrium of 1D Vlasov-Poisson system modeling electrostatic plasmas. A sharp linear instability criterion was obtained by Penrose in 1960. With C. Zeng, we constructed stable and unstable invariant manifolds near linearly unstable homogeneous states. This implies the nonlinear instability in the macroscopic sense. There is no restriction on the homogeneous profiles. In particular, we can treat the cases with vanishing or compactly supported steady distribution functions, which were excluded in the previous study of nonlinear instability. |
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