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

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

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 = 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.
Original languageEnglish
Pages (from-to)1 - 28
Number of pages28
JournalClassical and Quantum Gravity
Volume29
Issue number15
DOIs
Publication statusPublished - 2012

Cite this