Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 19 min ago
PreprintarXiv licencearXiv

Maximal regularity for the Stokes operator in bounded C1 domains

  • Su Liang
Open at sourcePDFDOICite

Abstract

Let Ω be a bounded C1 domain in ℝd, d≥2. We establish vector-valued resolvent estimates for the Dirichlet Stokes system in Lq(Ω;ℓ2) for every 1<q<∞. The estimates are uniform in the number and choice of spectral parameters in any fixed sector avoiding the negative real axis. These estimates imply that the Stokes operator is ℛ-sectorial of angle zero and has maximal Lr-regularity for every 1<r<∞. Our proof builds on the perturbation approach of Geng and Shen, with a different half-space argument to handle independently varying spectral parameters.

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. Optimal regularity and fine asymptotics for very fast diffusion equations in bounded domains
    Tianling Jin, Xushan Tu, Jingang Xiong +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Sharp regularity and small ball probabilities for the stochastic heat equation on bounded domains
    Jingwu Hu, Cheuk Yin Lee
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  4. Maximal Lp-Lq regularity of finite element methods for stochastic parabolic equations in polygonal domains
    Genming Bai, Jianbo Cui, Buyang Li
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  5. Generalized Logarithmic Sobolev inequalities on Bounded Domains and exponential decay to Boltzmann states for Nernst--Planck--Navier--Stokes systems
    Elie Abdo
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{liang2026maximal,
  title = {{Maximal regularity for the Stokes operator in bounded $C^1$ domains}},
  author = {Su Liang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04464},
  eprint = {2611.04464},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04464},
}
RIS
TY  - UNPB
TI  - Maximal regularity for the Stokes operator in bounded C^1 domains
AU  - Su Liang
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04464
UR  - https://arxiv.org/abs/2611.04464
AB  - Let Ω be a bounded C^1 domain in ℝ^d, d≥2. We establish vector-valued resolvent estimates for the Dirichlet Stokes system in L^q(Ω;ℓ^2) for every 1<q<∞. The estimates are uniform in the number and choice of spectral parameters in any fixed sector avoiding the negative real axis. These estimates imply that the Stokes operator is ℛ-sectorial of angle zero and has maximal L^r-regularity for every 1<r<∞. Our proof builds on the perturbation approach of Geng and Shen, with a different half-space argument to handle independently varying spectral parameters.
ER  -