Local smooth solutions of the relativistic Euler equation. II (Q1906565)

This paper deals with the motion of a barotropic relativistic perfect fluid in a Minkowski space-time. The objective is to extend a previous result on existence and uniqueness obtained by the authors for state equation of the form \(p(\rho)= a^2 \rho^\gamma\) with \(0<a<c\) and \(\gamma>1\) \((c\) is the speed of light, \(p\) is the pressure, \(\rho\) is the density) to a more general state equation. More specifically, these new assumptions are \(p(\rho)\in C^\infty (\rho_*, \rho^*)\), \(p(\rho) >0\), \(0<p' (\rho)<c^2\) for \(\rho\in (\rho_*, \rho^*)\), where \(\rho_* \geq 0\) and \(\rho^* \in [0,\infty]\) \((\rho^* >\rho_*)\) are given constants. The main result of the paper is an existence and uniqueness theorem under suitable functional assumption, and boundedness requirements upon the initial data.