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

Batt, J.; Joern, E. und Skubachevskii, A. L. (2020): Stationary Spherically Symmetric Solutions of the Vlasov-Poisson System in the Three-Dimensional Case. In: Doklady Mathematics, Bd. 102, Nr. 1: S. 265-268

Abstract

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1064-5624
• Sprache: Englisch