Global solutions of the relativistic Euler equations
We demonstrate the existence of solutions with shocks for the equations describing a perfect fluid in special relativity, namely, \(\text{div }T=0\), where \(T^{ij}=(p+\rho c^ 2)u^ i u^ j+p\eta^{ij}\) is the stress energy tensor for the fluid. Here, \(p\) denotes the pressure, \(u\) the 4-velocity, \(\rho\) the mass-energy density of the fluid, \(\eta^{ij}\) the flat Minkowski metric, and \(c\) the speed of light. We assume that the equation of state is given by \(p=\sigma^ 2\rho\), where \(\sigma^ 2\), the sound speed, is constant. For these equations, we construct bounded weak solutions of the initial value problem in two- dimensional Minkowski spacetime, for any initial data of finite total variation.
scientific article; zbMATH DE number 464945
scientific article