Stability of Riemann solutions with large oscillation for the relativistic Euler equations

S. Bianchini, A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems, Preprint, 2001. Bressan, 2000 Chang, 1989, The Riemann Problem and Interaction of Waves in Gas Dynamics, Vol. 41 Chen, 2000, Vacuum states and global stability of rarefaction waves for compressible flow, Methods Appl. Anal., 7, 75, 10.4310/MAA.2000.v7.n2.a5 Chen, 1999, Large-time behavior of entropy solutions of conservation laws, J. Differential Equations, 152, 308, 10.1006/jdeq.1998.3527 Chen, 1999, Divergence-measure fields and hyperbolic conservation laws, Arch. Rational Mech. Anal., 147, 89, 10.1007/s002050050146 Chen, 2000, Uniqueness and asymptotic stability of Riemann solutions for the compressible Euler equations, Trans. Amer. Math. Soc., 353, 1103, 10.1090/S0002-9947-00-02660-X Chen, 2003, Extended divergence-measure fields and the Euler equations for gas dynamics, Comm. Math. Phys., 236, 251, 10.1007/s00220-003-0823-7 Chen, 2002, Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics, Comm. Math. Phys., 228, 201, 10.1007/s002200200615 G.-Q. Chen, P. LeFloch, Existence theory for the relativistic Euler equations, in preparation, 2004. Chen, 2000, Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws, Arch. Rational Mech. Anal., 153, 205, 10.1007/s002050000081 G.-Q. Chen, D. Wang, The Cauchy Problem for the Euler Equations for Compressible Fluids, Handbook of Mathematical Fluid Dynamics, Vol. 1, Elsevier Science B.V, Amsterdam, The Netherlands, 2002, pp. 421–543. Chen, 1995, Conservation laws for the relativistic p-system, Comm. Partial Differential Equations, 20, 1605, 10.1080/03605309508821145 Dafermos, 1989, Generalized characteristics in hyperbolic systems of conservation laws, Arch. Rational Mech. Anal., 107, 127, 10.1007/BF00286497 Dafermos, 1996, Entropy and the stability of classical solutions of hyperbolic systems of conservation laws, 1640, 48 Dafermos, 1999 DiPerna, 1979, Uniqueness of solutions to hyperbolic conservation laws, Indiana Univ. Math. J., 28, 137, 10.1512/iumj.1979.28.28011 Filippov, 1960, Differential equations with discontinuous right-hand side, Mat. Sb. (N.S.), 51, 99 Glimm, 1965, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18, 95, 10.1002/cpa.3160180408 P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, CBMS, Vol. 11, SIAM, Philadelphia, 1973. LeFloch, 2002 Lewick, 2002, On the L1 well posedness of systems of conservation laws near solutions containing two large shocks, J. Differential Equations, 179, 133, 10.1006/jdeq.2000.4000 Li, 2003, Global stability of solutions with discontinuous initial data containing vacuum states for the isentropic Euler equations, Z. Angew. Math. Phys., 54, 1 Liu, 1999, Well-posedness theory for hyperbolic conservation laws, Comm. Pure Appl. Math., 52, 1553, 10.1002/(SICI)1097-0312(199912)52:12<1553::AID-CPA3>3.0.CO;2-S Serre, 2000 Smoller, 1983 Smoller, 1993, Global solutions of the relativistic Euler equations, Comm. Math. Phys., 156, 67, 10.1007/BF02096733 Taub, 1957, Approximate solutions of the Einstein equations for isentropic motions of plane symmetric distributions of perfect fluids, Phys. Rev., 107, 884, 10.1103/PhysRev.107.884 Thompson, 1986, The special relativistic shock tube, J. Fluid Mech., 171, 365, 10.1017/S0022112086001489 Thorne, 1973, Relativistic shocks, Astrophys. J., 179, 897, 10.1086/151927 Volpert, 1967, The space BV and quasilinear equations, Mat. Sb. (N.S.), 73, 255 Weinberg, 1972