Stability Issues in the Quasineutral Limit of the One-Dimensional Vlasov–Poisson Equation

@article{HanKwan2015StabilityII,
  title={Stability Issues in the Quasineutral Limit of the One-Dimensional Vlasov–Poisson Equation},
  author={Daniel Han-Kwan and M. Hauray},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={334},
  pages={1101-1152}
}
This work is concerned with the quasineutral limit of the one-dimensional Vlasov–Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is threefold: first, we provide a proof of the fact that the formal limit does not hold for homogeneous profiles that satisfy the Penrose instability criterion. Second, we prove on the other hand that the limit is true for homogeneous profiles that satisfy some monotonicity condition, together with a symmetry condition. We… Expand
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