Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 11 min ago
PreprintCC BY 4.0arXiv

Global well-posedness for the compressible Navier-Stokes equations with vacuum and smallness on coefficient-coupled scaling invariant quantity

  • Hao Xu
  • Xin Zhong
Open at sourcePDFDOICite

Abstract

We investigate the Cauchy problem of three-dimensional compressible Navier-Stokes equations with far-field vacuum. Based on delicate energy estimates and structures of the systems under consideration, we show the global well-posedness and decay rates of strong solutions provided that some coefficient-coupled scaling invariant initial quantity is suitably small. In particular, our smallness conditions are independent of any initial data and known parameters in the systems. Moreover, there is no need to require the compatibility conditions on the initial data. Our results improve previous works.

Related

  1. Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition
    Lin Xu, Xin Zhong
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Global Well-Posedness and Large Time Asymptotic Behavior of Strong Solutions to the Compressible Viscous Non-Resistive MHD Equations with Vacuum
    Jiaxu Li, Boqiang Lü, Bing Yuan
    arXivPreprintCC0Full textAnalysis & PDEsarXiv
  3. Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit
    Timothée Crin-Barat, Xinghong Pan, Ling-Yun Shou +1
    HALPreprintCC BY 4.0Full textGeneral mathematicsHAL
  4. Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping
    Liening Qiao, Jiahong Wu, Fuyi Xu +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
    Marco Artiano, Kieran Ricardo, Oswald Knoth +2
    arXivPreprintCC BY 4.0Full textAtmospheric science & meteorologyNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{xu2026global,
  title = {{Global well-posedness for the compressible Navier-Stokes equations with vacuum and smallness on coefficient-coupled scaling invariant quantity}},
  author = {Hao Xu and Xin Zhong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.16238},
  eprint = {2606.16238},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16238},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global well-posedness for the compressible Navier-Stokes equations with vacuum and smallness on coefficient-coupled scaling invariant quantity
AU  - Hao Xu
AU  - Xin Zhong
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2606.16238
UR  - https://arxiv.org/abs/2606.16238
AB  - We investigate the Cauchy problem of three-dimensional compressible Navier-Stokes equations with far-field vacuum. Based on delicate energy estimates and structures of the systems under consideration, we show the global well-posedness and decay rates of strong solutions provided that some coefficient-coupled scaling invariant initial quantity is suitably small. In particular, our smallness conditions are independent of any initial data and known parameters in the systems. Moreover, there is no need to require the compatibility conditions on the initial data. Our results improve previous works.
ER  -