TY - JOUR

T1 - On the existence of solutions to the relativistic Euler equations in two spacetime dimensions with a vacuum boundary

AU - Oliynyk, Todd

PY - 2012

Y1 - 2012

N2 - We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in two spacetime dimensions with an equation of state of the form p = K rho(2) that have a fluid vacuum boundary. Near the fluid vacuum boundary, the sound speeds for these solutions are monotonically decreasing, approaching zerowhere the density vanishes. Moreover, the fluid acceleration is finite and bounded away from zero as the fluid vacuum boundary is approached. The existence results of this paper also generalize in a straightforward manner to equations of state of the form p = K rho(gamma+1/gamma) with gamma > 0.

AB - We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in two spacetime dimensions with an equation of state of the form p = K rho(2) that have a fluid vacuum boundary. Near the fluid vacuum boundary, the sound speeds for these solutions are monotonically decreasing, approaching zerowhere the density vanishes. Moreover, the fluid acceleration is finite and bounded away from zero as the fluid vacuum boundary is approached. The existence results of this paper also generalize in a straightforward manner to equations of state of the form p = K rho(gamma+1/gamma) with gamma > 0.

U2 - 10.1088/0264-9381/29/15/155013

DO - 10.1088/0264-9381/29/15/155013

M3 - Article

SN - 0264-9381

VL - 29

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 15

M1 - 155013

ER -