Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids

Marcelo M. Disconzi, Vu Hoang, Maria Radosz

Published 2020-08-09Version 1

We consider equations of M\"uller-Israel-Stewart type describing a relativistic viscous fluid with bulk viscosity in four-dimensional Minkowski space. We show that there exists a class of smooth initial data that are localized perturbations of constant states for which the corresponding unique solutions to the Cauchy problem breakdown in finite time. Specifically, we prove that in finite time such solutions develop a singularity or become unphysical in a sense that we make precise. We also show that in general Riemann invariants do not exist in $1+1$ dimensions for physically relevant equations of state and viscosity coefficients.