Analytical Solutions to the Cylindrically Symmetric Compressible Euler–Euler System Coupled Through a Drag Force

ABSTRACT In this paper, we study the compressible Euler–Euler system coupled through a relaxation drag force in three‐dimensional space. In the case of cylindrical symmetry, we assume that the radial velocity and the angular velocity of one fluid are both equal to the ones of the other, respectively, which leads to that the drag force affects the two fluids only along the axil direction. By using some ansatzs, we present two classes of global analytical solutions for the isothermal fluid: one pulsates periodically except for the two axial velocities, the other decays to zero as time tends to infinity.