Partial Regularity for Stationary Navier-Stokes Systems by the Method of \(\mathcal{A}\)-Harmonic Approximation

Acta Mathematica Scientia volume 40, pages835–854(2020)Cite this article

Abstract

In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the \(\mathcal{A}\)-harmonic approximation technique. In this article, we extend the result of Shuhong Chen and Zhong Tan [7] and Giaquinta and Modica [18] to the stationary Navier-Stokes system with subquadratic growth.

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Author information

Affiliations

  1. School of Mathematical Sciences, Xiamen University, Fujian, 361005, China

    Yichen Dai 戴神深

  2. School of Mathematical Science and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian, 361005, China

    Zhong Tan 谭忠

Authors
  1. Yichen Dai 戴神深
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  2. Zhong Tan 谭忠
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Corresponding authors

Correspondence to Yichen Dai 戴神深 or Zhong Tan 谭忠.

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Dai, Y., Tan, Z. Partial Regularity for Stationary Navier-Stokes Systems by the Method of \(\mathcal{A}\)-Harmonic Approximation. Acta Math Sci 40, 835–854 (2020). https://doi.org/10.1007/s10473-020-0317-0

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Key words

  • Stationary Navier-Stokes systems
  • controllable growth condition
  • partial regularity
  • \(\mathcal{A}\)-harmonic approximation

2010 MR Subject Classification

  • 35J60
  • 35Q30
  • 76N10