Global Entropy Solutions of the Cauchy Problem for Nonhomogeneous Relativistic Euler System*

Abstract

We analyze the 2 × 2 nonhomogeneous relativistic Euler equations for perfect fluids in special relativity. We impose appropriate conditions on the lower order source terms and establish the existence of global entropy solutions of the Cauchy problem under these conditions.

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

“…System (1) models the dynamics of plane waves in special relativistic fluids [1,3,11,15,[17][18][19][20][21][22][23][24][25][26][30][31][32][33]35] in a twodimensional Minkowski space-time (x 0 , x 1 ): div T = 0, with the stress-energy tensor for the fluid:…”

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).…”

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

“…The equation of state is For a perfect fluid, p(ρ) = κ 2 ρ γ , γ ≥ 1, where γ = 1 models an isothermal gas and γ > 1 a polytropic gas, and κ is the speed of sound satisfying κ < c. System (1.1) models the dynamics of plane waves in special relativistic fluids (see [1,3,5,11,14,[16][17][18][19][20][21][22][23][24][25][26][29][30][31][32]) in a two-dimensional Minkowski space-time (x 0 , x 1 ):…”