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

Ariel Lerman, Marcelo M. Disconzi, Jorge Noronha

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number015201
JournalJournal of Physics A: Mathematical and Theoretical
Volume57
Issue number1
DOIs
StatePublished - Jan 5 2024

Keywords

  • Israel-Stewart fluid dynamics
  • local well-posedness
  • singularity formation
  • viscous fluid dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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