Preprint A566/2007
$\L1$ Stability of Spatially Periodic Solutions in Relativistic Gas Dynamics

Hermano Frid | Calvo, Daniela | Colombo, Rinaldo

**Keywords: **
relativistic gas dynamics | conservation laws | well-posedness | spatially periodic solutions

This paper proves the well posedness of spatially periodic
solutions of the relativistic isentropic gas dynamics equations. The pressure is given by a $\gamma$-law with initial data of large amplitude, provided $\gamma-1$ is sufficiently small. As a byproduct of our techniques, we obtain the same results for the classical case. At the limit $c \to +\infty$, the solutions of the relativistic system converge to the solutions of the classical one, the convergence rate being $1/c^2$. 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 $\gamma-1$ is small.