Stationary Spherically Symmetric Solutions of the Vlasov–Poisson System in the Three-Dimensional Case

Abstract: We consider the three-dimensional stationary Vlasov–Poisson system of equations with respect to the distribution function of the gravitating matter f=fq(r,u), the local density ρ=ρ(r), and the Newtonian potential U=U(r), where r:=|x|, u:= |v| ((x,v)ε ℝ3ℝ3 are the space–velocity coordinates), and f is a function q of the local energy E:= U(r) + u2/2. For a given function ρ=ρ(r), we obtain sufficient conditions for p to be “extendable.” This means that there exists a stationary spherically symmetric solution (fq,ρ,U) of the Vlasov–Poisson system depending on the local energy E such that ρ=ρ. © 2020, Pleiades Publishing, Ltd.