Spatially periodic solutions in relativistic isentropic gas dynamics

We consider the initial value problem, with periodic initial data, for the Euler equations in relativistic isentropic gas dynamics, for ideal polytropic gases which obey a constitutive equation, relating pressure p and density rho, p = kappa(2) rho(gamma), with gamma greater than or equal to 1, 0 < kappa < c, where c is the speed of light. Global existence of periodic entropy solutions for initial data sufficiently close to a constant state follows from a celebrated result of Glimm and Lax (1970). We prove that given any periodic initial data of locally bounded total variation, satisfying the physical restrictions 0 < inf(x is an element of R) rho(o)(x) < sup(xis an element ofR) rho(o)(x) < +infinity, parallel to nu(o)parallel to(infinity) < c, where v is the gas velocity, there exists a globally defined spatially periodic entropy solution for the Cauchy problem, if 1 less than or equal to gamma < gamma(o), for some gamma(o) > 1, depending on the initial bounds. The solution decays in L-loc(1) to its mean value as t --> infinity.