Abstract
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 = Kρ2 that have a fluid vacuum boundary. Near the fluid vacuum boundary, the sound speeds 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 paper also generalize in a straightforward manner to equations of state of the form with γ > 0.
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