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Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data. (English) Zbl 1228.35252
In this article the authors extend previous results giving the time decay of solutions of the Cauchy problem to the Vlasov-Poisson system with small initial data. They show in particular that the Bardos-Degond result
\[ \|\rho\|_{L^\infty}\leq C(1+t)^{-3}, \] for the density \(\rho(t,x)\) of particles in \(\mathbb R^3\), extends to higher-order derivatives
\[ \|D^k\rho\|_{L^\infty}\leq C(1+t)^{-3-k}, \] for any \(k\in\mathbb N\).

MSC:
35Q83 Vlasov equations
45K05 Integro-partial differential equations
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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