### Abstract

We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂
_{i}
v
_{i}
, i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂
_{r}
v
^{r}
is not bounded both below and above near a singular point, if it exists.

Original language | English |
---|---|

Pages (from-to) | 3185-3197 |

Number of pages | 13 |

Journal | Nonlinearity |

Volume | 23 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2010 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Nonlinearity*,

*23*(12), 3185-3197. https://doi.org/10.1088/0951-7715/23/12/010

}

*Nonlinearity*, vol. 23, no. 12, pp. 3185-3197. https://doi.org/10.1088/0951-7715/23/12/010

**On the behaviour of Navier-Stokes equations near a possible singular point.** / Kang, Kyungkeun; Lee, Jihoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the behaviour of Navier-Stokes equations near a possible singular point

AU - Kang, Kyungkeun

AU - Lee, Jihoon

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂ i v i , i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂ r v r is not bounded both below and above near a singular point, if it exists.

AB - We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂ i v i , i = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either p or ∂ r v r is not bounded both below and above near a singular point, if it exists.

UR - http://www.scopus.com/inward/record.url?scp=78650122217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650122217&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/23/12/010

DO - 10.1088/0951-7715/23/12/010

M3 - Article

VL - 23

SP - 3185

EP - 3197

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 12

ER -