Large-bulk-viscosity limit for two-dimensional compressible micropolar fluids with vacuum
Abstract
We consider the Cauchy problem for the two-dimensional compressible micropolar fluid system on the torus 𝕋2. The initial density is bounded and nonnegative and may contain vacuum, while the initial velocity and microrotation belong to H1(𝕋2). For sufficiently large bulk viscosity ν, we prove the global-in-time existence of solutions without a smallness assumption on the H1 size of the data, provided that the initial compressible component is well prepared in the sense that √ν|divu0|L2 is uniformly bounded. The proof combines the effective viscous flux with a coupled energy scheme that exploits the vorticity--microrotation dissipation at both the basic and material-derivative levels. For the linear pressure law, we also prove uniqueness in the stated solution class by means of a coupled backward parabolic problem, logarithmic interpolation, and Osgood's lemma. For fixed initial data with divu0=0, we also justify the limit ν→∞: every sequence of the corresponding solutions admits a subsequence converging to a solution of the two-dimensional inhomogeneous incompressible micropolar system.
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BibTeX
@misc{du2026largebulkviscosity,
title = {{Large-bulk-viscosity limit for two-dimensional compressible micropolar fluids with vacuum}},
author = {Zijian Du and Sen Yang and Xinglong You},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37099},
eprint = {2610.37099},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37099},
}
RIS
TY - UNPB
TI - Large-bulk-viscosity limit for two-dimensional compressible micropolar fluids with vacuum
AU - Zijian Du
AU - Sen Yang
AU - Xinglong You
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37099
UR - https://arxiv.org/abs/2610.37099
AB - We consider the Cauchy problem for the two-dimensional compressible micropolar fluid system on the torus 𝕋^2. The initial density is bounded and nonnegative and may contain vacuum, while the initial velocity and microrotation belong to H^1(𝕋^2). For sufficiently large bulk viscosity ν, we prove the global-in-time existence of solutions without a smallness assumption on the H^1 size of the data, provided that the initial compressible component is well prepared in the sense that √ν|divu_0|_L^2 is uniformly bounded. The proof combines the effective viscous flux with a coupled energy scheme that exploits the vorticity--microrotation dissipation at both the basic and material-derivative levels. For the linear pressure law, we also prove uniqueness in the stated solution class by means of a coupled backward parabolic problem, logarithmic interpolation, and Osgood's lemma. For fixed initial data with divu_0=0, we also justify the limit ν→∞: every sequence of the corresponding solutions admits a subsequence converging to a solution of the two-dimensional inhomogeneous incompressible micropolar system.
ER -