Geodesic
Stationary spherically symmetric solutions of the Vlasov–Poisson system in the three-dimensional case
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 5-8 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the three-dimensional stationary Vlasov–Poisson system of equations with respect to the distribution function of the gravitating matter $f=f_q(r,u)$, the local density $\rho=\rho(r)$, and the Newtonian potential $U=U(r)$, where $r:=|x|$, $u:=|v|$ ($(x,v)\in\mathbb R^3\times\mathbb R^3$ are the space–velocity coordinates), and $f$ is a function $q$ of the local energy $E:=U(r)+\dfrac{u^2}2$. For a given function $p=p(r)$, we obtain sufficient conditions for $p$ to be “extendable”. This means that there exists a stationary spherically symmetric solution $(f_q,\rho,U)$ of the Vlasov–Poisson system depending on the local energy $E$ such that $\rho=p$.
Mots-clés : Vlasov–Poisson system
Keywords: stationary spherically symmetric solution, stellar dynamics. 
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     title = {Stationary spherically symmetric solutions of the {Vlasov{\textendash}Poisson} system in the three-dimensional case},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
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     year = {2020},
     volume = {493},
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J. Batt; E. Jörn; A. L. Skubachevskii. Stationary spherically symmetric solutions of the Vlasov–Poisson system in the three-dimensional case. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 5-8. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a0/

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