On the Steady State Relativistic Euler-Poisson Equations

Singularity formation for the relativistic Euler‐Poisson equations with repulsive force and damping

“…Under certain monotonic conditions on initial data, and by using an invariant of Lax's method, Geng and Wang [6] obtained the global existence of a smooth solution of initial value problem for one-dimensional relativistic Euler-Poisson equations with repulsive force. Mai, Li, and Zhang [7] proved the existence and uniqueness of smooth solutions for the one-dimensional steady state relativistic Euler-Poisson equations with relaxation. Subsequently, they [8] also considered the asymptotic limits of solutions to the initial boundary value problem of the relativistic Euler-Poisson equations.…”

Blowup of regular solutions for the relativistic Euler–Poisson equations

“…Due to the complexity of the structures of system (1), research on multi-dimensional relativistic Euler-Poisson equations is still at an early stage. In 2013, Mai, Li and Zhang [7] gave the first wellposed result for the steady-state relativistic Euler-Poisson equations with relaxation. For system (1) in the one dimensional case, Geng and Wang [3] obtained the global existence of a smooth solution with some monotonic conditions on the initial data.…”