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

2023/07/13 by Ariel Lerman, Lerman, Ariel, Marcelo M. Disconzi +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nuclear Theory (nucl-th)

paper · pdf · doi:10.48550/arxiv.2307.09611

openalex publication_date 2023/07/13 · openalex created_date 2023/07/21 · openalex updated_date 2026/07/28

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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