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

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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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