### Abstract

We consider discontinuous influx for the Navier–Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension larger than or equal to two. This is an extension of the result in [T. Chang and H. Choe, J. Differential Equations, 254 (2013), pp. 2682–2704] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. If the normal component of bounded boundary data is Dini-continuous in space or log-Dini-continuous in time, then the constructed solution becomes bounded and a maximum modulus estimate is valid.

Original language | English |
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Pages (from-to) | 3147-3171 |

Number of pages | 25 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

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*SIAM Journal on Mathematical Analysis*, vol. 50, no. 3, pp. 3147-3171. https://doi.org/10.1137/17M1152565

**On maximum modulus estimates of the navier–stokes equations with nonzero boundary data.** / Chang, Tongkeun; Choe, Hi Jun; Kang, Kyungkeun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On maximum modulus estimates of the navier–stokes equations with nonzero boundary data

AU - Chang, Tongkeun

AU - Choe, Hi Jun

AU - Kang, Kyungkeun

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider discontinuous influx for the Navier–Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension larger than or equal to two. This is an extension of the result in [T. Chang and H. Choe, J. Differential Equations, 254 (2013), pp. 2682–2704] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. If the normal component of bounded boundary data is Dini-continuous in space or log-Dini-continuous in time, then the constructed solution becomes bounded and a maximum modulus estimate is valid.

AB - We consider discontinuous influx for the Navier–Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension larger than or equal to two. This is an extension of the result in [T. Chang and H. Choe, J. Differential Equations, 254 (2013), pp. 2682–2704] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. If the normal component of bounded boundary data is Dini-continuous in space or log-Dini-continuous in time, then the constructed solution becomes bounded and a maximum modulus estimate is valid.

UR - http://www.scopus.com/inward/record.url?scp=85049559255&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049559255&partnerID=8YFLogxK

U2 - 10.1137/17M1152565

DO - 10.1137/17M1152565

M3 - Article

AN - SCOPUS:85049559255

VL - 50

SP - 3147

EP - 3171

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 3

ER -