Analytical solutions to the cylindrically symmetric compressible isothermal Euler-Poisson equations of galaxies

Abstract In this paper, we study the cylindrically symmetric compressible isothermal Euler-Poisson equations of gaseous stars with a negative cosmological constant. By using some ansatzs, we construct a family of analytical periodic solutions to the system, which partially complements the result in [2009 Class. Quantum Grav. 26 235011], where a family of analytical periodic solutions to the system with spherical symmetry were given for the adiabatic exponent γ = 4/3. Our result may provide an explanation about the dynamical evolution of the cylindrically symmetric galaxies or interstellar clouds.