TY - JOUR
T1 - Local well-posedness and singularity formation in non-Newtonian compressible fluids
AU - Lerman, Ariel
AU - Disconzi, Marcelo M.
AU - Noronha, Jorge
N1 - The authors thank L Gavassino for discussions. A L thanks the Barry M Goldwater Scholarship for support. M M D is partially supported by NSF Grant DMS-2107701, a Chancelor\u2019s Faculty Fellowship, and a Vanderbilt Seeding Success Grant. J N is partially supported by the U.S. Department of Energy, Office of Science, Office for Nuclear Physics under Award Nos. DE-SC0021301 and DE-SC0023861. M M D and J N thank the KITP Santa Barbara for its hospitality during \u2018The Many Faces of Relativistic Fluid Dynamics\u2019 Program, where this work\u2019s last stages were completed. This research was partly supported by the National Science Foundation under Grant No. NSF PHY-1748958.
PY - 2024/1/5
Y1 - 2024/1/5
N2 - 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.
AB - 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.
KW - Israel-Stewart fluid dynamics
KW - local well-posedness
KW - singularity formation
KW - viscous fluid dynamics
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U2 - 10.1088/1751-8121/ad0fb4
DO - 10.1088/1751-8121/ad0fb4
M3 - Article
AN - SCOPUS:85180103477
SN - 1751-8113
VL - 57
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 1
M1 - 015201
ER -