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 language | English (US) |
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Article number | 015201 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 57 |
Issue number | 1 |
DOIs | |
State | Published - Jan 5 2024 |
Externally published | Yes |
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