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

Kyungkeun Kang; Jihoon Lee

doi:10.1088/0951-7715/23/12/010

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

Kyungkeun Kang, Jihoon Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂_iv _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 ∂_rv^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	https://doi.org/10.1088/0951-7715/23/12/010
Publication status	Published - 2010 Dec

All Science Journal Classification (ASJC) codes

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

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10.1088/0951-7715/23/12/010

Cite this

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abstract = "We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂iv 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 ∂rvr is not bounded both below and above near a singular point, if it exists.",

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AB - We show that if a singularity of suitable weak solutions to Navier-Stokes equations occurs, then either p or at least two of ∂iv 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 ∂rvr is not bounded both below and above near a singular point, if it exists.

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

Abstract

All Science Journal Classification (ASJC) codes

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