### 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