### Abstract

We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class L^{p,q} with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

Original language | English |
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Pages (from-to) | 955-987 |

Number of pages | 33 |

Journal | Communications in Partial Differential Equations |

Volume | 29 |

Issue number | 7-8 |

DOIs | |

Publication status | Published - 2004 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Communications in Partial Differential Equations*, vol. 29, no. 7-8, pp. 955-987. https://doi.org/10.1081/PDE-200033743

**On boundary regularity of the Navier-Stokes equations.** / Kang, Kyungkeun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On boundary regularity of the Navier-Stokes equations

AU - Kang, Kyungkeun

PY - 2004/7/1

Y1 - 2004/7/1

N2 - We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

AB - We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=8744221345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8744221345&partnerID=8YFLogxK

U2 - 10.1081/PDE-200033743

DO - 10.1081/PDE-200033743

M3 - Article

VL - 29

SP - 955

EP - 987

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 7-8

ER -