Plane steady shock waves in Israel-Stewart fluids
The authors study the existence of plane steady shock waves for relativistic dissipative fluids in the framework of the Israel-Stewart theory. Here shock waves are meant as continuous, single-valued, stable solutions connecting two asymptotic (in space) equilibrium states. They prove by means of algebraic computations that such solutions do not exist if the shock is sufficiently strong, i.e, if the upstream Mach number \(M^-=v(-\infty)/v_ s(-\infty)\), \(v_ s=[(\partial p/\partial \rho)_ s]^{1/2}\), is larger than some bound (or if the downstream Mach number \(M^+=v(+\infty)/v_ s(+\infty)\), is smaller than some bound). The reason is that at such bounds solutions become multiple- valued (some dynamical system degenerates), since the fluid velocity at some point in the shock becomes characteristic.
continuous, single-valued, stable solutions
scientific article; zbMATH DE number 4204055