### Abstract

We prove that a solution to Navier-Stokes equations is inL^{2}(0,∞:H^{2}(Ω)) under the critical assumption thatu∈L^{r,r′}, 3/r+2/r′≤1 withr≥3. A boundaryL^{∞}estimate for the solution is derived if the pressure on the boundary is bounded. Here our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate forL^{∞}-norm ofu. Moreover the solution isC^{1,α}continuous up to boundary if the tangential derivatives of the pressure on the boundary are bounded. Then, from the bootstrap argument a local higher regularity theorem follows, that is, the velocity is as regular as the boundary data of the pressure.

Original language | English |
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Pages (from-to) | 211-247 |

Number of pages | 37 |

Journal | Journal of Differential Equations |

Volume | 149 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1998 Nov 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Differential Equations*, vol. 149, no. 2, pp. 211-247. https://doi.org/10.1006/jdeq.1998.3481

**Boundary Regularity of Weak Solutions of the Navier-Stokes Equations.** / Choe, Hi Jun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boundary Regularity of Weak Solutions of the Navier-Stokes Equations

AU - Choe, Hi Jun

PY - 1998/11/1

Y1 - 1998/11/1

N2 - We prove that a solution to Navier-Stokes equations is inL2(0,∞:H2(Ω)) under the critical assumption thatu∈Lr,r′, 3/r+2/r′≤1 withr≥3. A boundaryL∞estimate for the solution is derived if the pressure on the boundary is bounded. Here our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate forL∞-norm ofu. Moreover the solution isC1,αcontinuous up to boundary if the tangential derivatives of the pressure on the boundary are bounded. Then, from the bootstrap argument a local higher regularity theorem follows, that is, the velocity is as regular as the boundary data of the pressure.

AB - We prove that a solution to Navier-Stokes equations is inL2(0,∞:H2(Ω)) under the critical assumption thatu∈Lr,r′, 3/r+2/r′≤1 withr≥3. A boundaryL∞estimate for the solution is derived if the pressure on the boundary is bounded. Here our estimate is local. Indeed, employing Moser type iteration and the reverse Hölder inequality, we find an integral estimate forL∞-norm ofu. Moreover the solution isC1,αcontinuous up to boundary if the tangential derivatives of the pressure on the boundary are bounded. Then, from the bootstrap argument a local higher regularity theorem follows, that is, the velocity is as regular as the boundary data of the pressure.

UR - http://www.scopus.com/inward/record.url?scp=0039500607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039500607&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1998.3481

DO - 10.1006/jdeq.1998.3481

M3 - Article

AN - SCOPUS:0039500607

VL - 149

SP - 211

EP - 247

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -