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arXiv · 2307.09611

Local well-posedness and singularity formation in non-Newtonian compressible fluids

Ariel Lerman·Marcelo M. Disconzi·Jorge Noronha
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Abstract

We investigate the initial value problem of a very general class of $3+1$ non-Newtonian compressible fluids in which the viscous stress tensor with shear and bulk viscosity relaxes to its Navier-Stokes values. These fluids correspond to the non-relativistic limit of well-known Israel-Stewart-like theories used in the relativistic fluid dynamic simulations of high-energy nuclear and astrophysical systems. After establishing the local well-posedness of the Cauchy problem, we show for the first time in the literature that there exists a large class of initial data for which the corresponding evolution breaks down in finite time due to the formation of singularities. This implies that a large class of non-Newtonian fluids do not have finite solutions defined at all times.

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Ariel Lerman, Marcelo M. Disconzi, Jorge Noronha. 2023-07-13. Local well-posedness and singularity formation in non-Newtonian compressible fluids. https://arxiv.org/abs/2307.09611

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