New flux conservative formulation of viscous fluid dynamics and the fate of shocks

The existence and formation of shock solutions to relativistic ideal fluids have been investigated extensively for decades [1]. The relativistic Euler equations allow for shock formation as a physical solution by admitting weak solutions to the conservation law equations of motion. However, the relativistic Euler equations do not describe viscous processes. The BDNK approach [2-5] to viscous relativistic fluids describes the most general formulation of dissipation in fluids up to first order in derivatives. While shock solution profiles can exist in this theory [6], it is unclear if shocks form in this effective theory within its regime of validity. Using a new, fully-flux conservation formulation of the BDNK equations, we study shocks in relativistic, dissipative fluids in a consistent fashion. We present new results on 1+1 numerical simulations of the BDNK equations using initial data with maximum overlap with the conditions for shock formation in an ideal fluid to determine the fate of shocks in viscous relativistic fluids.

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[4] F. S. Bemfica, F. S. Bemfica, M. M. Disconzi, Phys. Rev. D 100, 104020 (2019).

[5] F. S. Bemfica, M. M. Disconzi, and J. Noronha, Phys. Rev. X 12, 021044 (2022).

[6] H. Freistuhler, Phys. Rev. D 103, 124045 (2021).