SELF-SIMILAR SOLUTIONS OF THE RELATIVISTIC EULER SYSTEM WITH SPHERICAL SYMMETRY

We consider the spherical piston problem in relativistic fluid dynamics. When the spherical piston expands at a constant speed, we show that the self-similar solution with a shock front exists under the relativistic principle that all velocities are bounded by the light speed. The equation of state is given by P = σ²ρ, where σ, the sound speed, is a constant. It is an important model describing the evolution of stars. Also, we present the global existence of BV solutions for the relativistic Euler system given that the piston speed is perturbed around a constant in a finite time interval. The analysis is based on the modified Glimm scheme and the smallness assumption is required on the initial data.