Existence and Stability of Equilibrium Solutions of the Vlasov Equation with a Modified Gravitational Potential

Abstract—We consider a system of mutually gravitating particles with possible collisions, which is modeled by supplementing the gravitational potential with the potential of repulsive forces similar to Lennard-Jones intermolecular forces. For an infinite number of particles, the probability density function is determined by the Vlasov kinetic equation with a modified gravitational potential. The existence of a large class of nonlinearly stable equilibrium solutions of this equation is proved using the energy–Casimir method.