LAUSR

Abstract The family of exact solutions with parameter λ of the 2D isothermal Euler-Poisson equations, which can be used to model the evolution of self-gravitating galaxies or gaseous stars, is investigated. By solving the Liouville equation in Yuen’s analytical solutions, a family of exact solutions is obtained for λ = 0 . We show that although such solutions remain local with finite mass and finite potential energy for all time, they have unbounded kinetic energy for any given time. In physics terms, these ( 2 + 1 ) -dimensional solutions may correspond to a ( 3 + 1 ) -dimensional model of an infinite universe with finite mass and infinite kinetic energy. We also show that the mass and kinetic energy of the solutions are finite for λ  ( 2 + 1 ) -dimensional case a universe model with finite total energy, provided that the finiteness of the potential energy is given.