Igor Kukavica 2009 Nonlinearity 22 2889 doi:10.1088/0951-7715/22/12/005
The fractal dimension of the singular set for solutions of the Navier–Stokes system
Igor Kukavica
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We consider suitable weak solutions of the Navier–Stokes system in a bounded space-time domain D. We prove that the parabolic fractal dimension of the singular set is less than or equal to 135/82. We also introduce the concept of the parabolic fractal measure 
and prove that the fractal measure 
of the singular set is zero. For the Leray–Hopf weak solutions, we prove 
, where ΣT denotes the set of singular times on [0, T] and 
stands for the 1/2-dimensional fractal measure.
- PACS
- MSC
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76D05 Navier-Stokes equations (See also 35Q30)
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
- Subjects
- Dates
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Issue 12 (December 2009)
Received 16 April 2009, in final form 29 September 2009
Published 30 October 2009
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The fractal dimension of the singular set for solutions of the Navier–Stokes system
Igor Kukavica 2009 Nonlinearity 22 2889
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