  We prove the existence of a wide class of solutions to the isentropic
relativistic Euler equations in 2 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 speed for these solutions are monotonically
decreasing, approaching zero where 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 article also generalize in a
straightforward manner to equations of state of the form
$p=K\rho^\frac{\gamma+1}{\gamma}$ with $\gamma > 0$.
