Global entropy solutions to the relativistic Euler equations for a class of large initial data

Abstract

We are concerned with global entropy solutions to the relativistic Euler equations for a class of large initial data which involve the interaction of shock waves and rarefaction waves. We first carefully analyze the global behavior of the shock curves, the rarefaction wave curves, and their corresponding inverse curves in the phase plane. Based on these analyses, we use the Glimm scheme to construct global entropy solutions to the relativistic Euler equations for the class of large discontinuous initial data. Mathematics Subject Classification (2000). Primary: 35B40, 35A05, 76Y05; Secondary: 35B35, 35L65, 85A05.

Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations

“…G. Q. Chen and Y. C. Li [4] established the uniqueness of Riemann solutions to the system (1.1) in the class of entropy solution in L ∞ ∩ BV loc with arbitrarily large oscillation, and then considered the uniqueness and stability of Riemann solutions with vacuum in the class of entropy solutions in L ∞ with large oscillation. In 2005, Y. C. Li et al [15] obtained the global existence of solutions to the isentropic relativistic Euler system using the Glimm scheme.…”

Non-relativistic global limits of entropy solutions to the extremely relativistic Euler equations

“…Due to the high complexity of the system itself, current efforts have been made mainly to the corresponding reduced 2 × 2 systems, involving either the conserved equations of baryon numbers and momentum or the conserved equations of momentum and energy(see [2][3][4][5]7,8,[10][11][12][13][14][15]19,[21][22][23][24][25]27,35,36] etc., and the references cited therein).…”

Dependence of entropy solutions in the large for the Euler equations on nonlinear flux functions

“…Due to the Lorenz invariance, if there are two states (ρ L , u L ) and (ρ R , u R ) connected by a shock, we can assume the velocity state of the left-hand side of the shock in the barred coordinates isū L = 0. Hence the Lax entropy and Rankine-Hugoniot conditions imply (see [6,8,17,19]…”