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Zbl 1168.35044
Calvo, Daniela; Colombo, Rinaldo M.; Frid, Hermano
$L^{1}$ stability of spatially periodic solutions in relativistic gas dynamics. (English)
[J] Commun. Math. Phys. 284, No. 2, 509-535 (2008). ISSN 0010-3616; ISSN 1432-0916/e

Summary: 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 $c \rightarrow + \infty$, 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.

MSC 2000:: *35Q75 PDE in relativity
76Y05 Nonclassical hydrodynamics
76N15 Gas dynamics, general
35B10 Periodic solutions of PDE
35B35 Stability of solutions of PDE
35A35 Theoretical approximation to solutions of PDE

Keywords: relativistic gas dynamics; periodic solutions; stability; approximate solutions

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