Features of a two-dimensional self-gravitating flow incident on a massive body

The features of a two-dimensional self-gravitating flow of particles incident on a massive body are investigated. A kinetic description of the system is considered using the Vlasov–Newton equation, taking into account both the gravitational field of the central object and the self-gravitation of the incident particles. As a result of the analysis, an expression is obtained for the viscosity due to self-gravitation, which turns out to be proportional to the square of the density and inversely proportional to the temperature. It is shown that the viscosity due to self-gravitation leads to non-Newtonian behavior of the medium. Based on the results obtained, some astrophysical problems are solved, such as one-dimensional stationary accretion of isothermal gas and the loss of angular momentum due to self-gravitation.