Local $\varepsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations

Xiufang Cui

Local $\varepsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations

Analysis of PDEs 2021-10-26 v1

Authors: Xiufang Cui

Abstract

In this paper, we establish $\varepsilon$ -regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations in both the unit ball $B_1$ and the unit half ball $B_1^+$ , respectively, which improve previous results in [J. Math. Fluid Mech., 6(2004), pp 78--101] and [Comm. Pure Appl. Math., 41(1988), pp 437--458]. The proofs of the main results are based on an iteration argument, Campanato's method, and interpolation techniques.

Keywords

navier-stokes equations epsilon-regularity suitable weak solutions stationary incompressible campanato method

Cite

@article{arxiv.2110.12600,
  title  = {Local $\varepsilon$-regularity criteria for the five dimensional stationary Navier-Stokes equations},
  author = {Xiufang Cui},
  journal= {arXiv preprint arXiv:2110.12600},
  year   = {2021}
}

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