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Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces

  • Chen Liang
  • Zhaonan Luo
  • Zhaoyang Yin
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Abstract

In this paper, we study the global regularity of the one-dimensional hypo-viscous compressible Navier--Stokes equations in the critical Besov spaces, where the initial data are close to the constant equilibrium state. We introduce an effective velocity, constructed as a combination of the density and the velocity, which is used to capture the high-frequency behavior of a. By performing elaborate high-frequency and low-frequency estimates together with a bootstrap argument, we obtain global existence for 1/2≤β<1. In particular, when 1/2≤β<3/4, we also prove the uniqueness of solutions. Furthermore, under an additional low-frequency assumption, we establish the optimal time decay rates.

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Cite

BibTeXRIS
BibTeX
@misc{liang2026global,
  title = {{Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces}},
  author = {Chen Liang and Zhaonan Luo and Zhaoyang Yin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25889},
  eprint = {2610.25889},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25889},
}
RIS
TY  - UNPB
TI  - Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces
AU  - Chen Liang
AU  - Zhaonan Luo
AU  - Zhaoyang Yin
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25889
UR  - https://arxiv.org/abs/2610.25889
AB  - In this paper, we study the global regularity of the one-dimensional hypo-viscous compressible Navier--Stokes equations in the critical Besov spaces, where the initial data are close to the constant equilibrium state. We introduce an effective velocity, constructed as a combination of the density and the velocity, which is used to capture the high-frequency behavior of a. By performing elaborate high-frequency and low-frequency estimates together with a bootstrap argument, we obtain global existence for 1/2≤β<1. In particular, when 1/2≤β<3/4, we also prove the uniqueness of solutions. Furthermore, under an additional low-frequency assumption, we establish the optimal time decay rates.
ER  -