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Batt, J.; Joern, E.; Skubachevskii, A. L. (2020): Stationary Spherically Symmetric Solutions of the Vlasov-Poisson System in the Three-Dimensional Case. In: Doklady Mathematics, Vol. 102, No. 1: pp. 265-268
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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: = vertical bar x vertical bar, u : vertical bar v vertical bar ((x, v) is an element of R-3 x R-3 are the space-velocity coordinates), and f is a function q of the local energy E: = u(r) + 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.