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 -