On Shock Profiles in Four-Field Formulations of Dissipative Relativistic Fluid Dynamics

This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors’ earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativistic dynamics of barotropic fluids in the presence of viscosity and heat conduction, shock waves of arbitrary strength have smooth, monotone dissipation profiles. The results and arguments extend classical considerations of Weyl (Comm. Pure Appl. Math. 2 (1949)) and Gilbarg (Amer. J. Math. 73 (1951)) to the relativistic setting. By contrast, for the related Bemfica-Disconzi-Noronha model (Phys. Rev. D 98 (2018)) many shocks have either no or only oscillatory profiles.