The combined limits of large bulk viscosity and small angular viscosity for the 2D compressible micropolar fluid equations
Abstract
This paper is concerned with the combined limits of large bulk viscosity and small angular viscosity for the two-dimensional compressible micropolar fluid equations. We first establish the global well-posedness of strong solutions to the Cauchy problem with large bulk viscosity, when the initial velocity is well-prepared in the sense that √ν|div u0|L2 is uniformly bounded. The global a priori estimates obtained are uniform with respect to both the bulk viscosity ν and the angular viscosity ε. Based on these uniform estimates, we then justify the combined limits as ν→∞ and ε→0, and show that the solutions of the compressible micropolar system converge to those of the viscous and non-diffusive incompressible micropolar system. The convergence rates for the incompressible limit and the vanishing angular viscosity limit are also derived. In particular, the convergence rate for the incompressible limit is shown to be of order ν−1/4 in general, and can be improved to ν−1/2 under an additional decay condition on the initial density. Compared with previous works, the vanishing angular viscosity limit is established without the extra technical assumption limε→0+ζ/εα<∞ for some 1/2≤ α<∞, which extends the relevant results from the incompressible case to the compressible setting. As a by-product, the global regularity of large solutions for the 2D compressible micropolar equations with/without angular viscosity is obtained, provided the bulk viscosity is large enough.
Related
- Large-bulk-viscosity limit for two-dimensional compressible micropolar fluids with vacuum
- Global Strong Solutions to the One-Dimensional Planar Compressible Magneto-Micropolar Equations with Vacuum
- Global existence of large strong solutions to the 3D compressible micropolar equations with density-dependent viscosities
- Uniqueness and stability of planar shock wave to 2D compressible Euler equations in the vanishing viscosity limit of compressible Navier-Stokes equations
- Singular viscosity-exponent limit for one-dimensional compressible Navier-Stokes equations with far field vacuum
BibTeX
@misc{lin2026combined,
title = {{The combined limits of large bulk viscosity and small angular viscosity for the 2D compressible micropolar fluid equations}},
author = {Fangbin Lin and Shengquan Liu and Jianwen Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15518},
eprint = {2609.15518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15518},
}
RIS
TY - UNPB
TI - The combined limits of large bulk viscosity and small angular viscosity for the 2D compressible micropolar fluid equations
AU - Fangbin Lin
AU - Shengquan Liu
AU - Jianwen Zhang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15518
UR - https://arxiv.org/abs/2609.15518
AB - This paper is concerned with the combined limits of large bulk viscosity and small angular viscosity for the two-dimensional compressible micropolar fluid equations. We first establish the global well-posedness of strong solutions to the Cauchy problem with large bulk viscosity, when the initial velocity is well-prepared in the sense that √ν|div u_0|_L^2 is uniformly bounded. The global a priori estimates obtained are uniform with respect to both the bulk viscosity ν and the angular viscosity ε. Based on these uniform estimates, we then justify the combined limits as ν→∞ and ε→0, and show that the solutions of the compressible micropolar system converge to those of the viscous and non-diffusive incompressible micropolar system. The convergence rates for the incompressible limit and the vanishing angular viscosity limit are also derived. In particular, the convergence rate for the incompressible limit is shown to be of order ν^−1/4 in general, and can be improved to ν^−1/2 under an additional decay condition on the initial density. Compared with previous works, the vanishing angular viscosity limit is established without the extra technical assumption lim_ε→0+ζ/ε^α<∞ for some 1/2≤ α<∞, which extends the relevant results from the incompressible case to the compressible setting. As a by-product, the global regularity of large solutions for the 2D compressible micropolar equations with/without angular viscosity is obtained, provided the bulk viscosity is large enough.
ER -