L1 Stability of Spatially Periodic Solutions in Relativistic Gas Dynamics

Abstract

This paper proves the well posedness of spatially periodic solutions of the relativistic isentropic gas dynamics equations. The pressure is given by a γ-law with initial data of large amplitude, provided γ − 1 is sufficiently small. As a byproduct of our techniques, we obtain the same results for the classical case. At the limit c → + ∞, the solutions of the relativistic system converge to the solutions of the classical one, the convergence rate being 1/c2. We also construct the semigroup of solutions of the Cauchy problem for initial data with bounded total variation, which can be large, as long as γ − 1 is small.