A uniqueness criterion for unbounded solutions to the Vlasov-Poisson system

Evelyne Miot

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arXiv · 1409.6988

A uniqueness criterion for unbounded solutions to the Vlasov-Poisson system

Evelyne Miot

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Abstract

We prove uniqueness for the Vlasov-Poisson system in two and three dimensions under the condition that the $L^p$ norms of the macroscopic density growth at most linearly with respect to $p$. This allows for solutions with logarithmic singularities. We provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow-up. In the gravitational two-dimensional case, such states are intimately related to radially symmetric steady solutions of the system. Our method relies on the Lagrangian formulation for the solutions, exploiting the second-order structure of the corresponding ODE.

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Evelyne Miot. 2014-09-24. A uniqueness criterion for unbounded solutions to the Vlasov-Poisson system. https://arxiv.org/abs/1409.6988

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