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
Show affiliationsRecommended by K Ohkitani
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
-
76D05 Navier-Stokes equations (See also 35Q30)
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
- Subjects
- Dates
-
Issue 12 (December 2009)
Received 16 April 2009, in final form 29 September 2009
Published 30 October 2009
-
The fractal dimension of the singular set for solutions of the Navier–Stokes system
Igor Kukavica 2009 Nonlinearity 22 2889
-
Scalar field theory and the definition of momentum in curved space
Simon Davis 2001 Class. Quantum Grav. 18 3395
-
Observation of Shubnikov–de Haas oscillations in the quasi-one-dimensional Bechgaard salt (TMTSF)2FSO3
O H Chung et al 2003 J. Phys.: Condens. Matter 15 7297
-
Magnetic atom optics: mirrors, guides, traps, and chips for atoms
E A Hinds and I G Hughes 1999 J. Phys. D: Appl. Phys. 32 R119
-
Detecting galactic binaries with LISA
Neil J Cornish and Edward K Porter 2005 Class. Quantum Grav. 22 S927
-
Fine resolution calculations of SAR in the human body for frequencies up to 3 GHz
P J Dimbylow 2002 Phys. Med. Biol. 47 2835
-
A rational function approximation of the singular eigenfunction of the monoenergetic neutron transport equation
A Sengupta 1984 J. Phys. A: Math. Gen. 17 2743
-
Conduction bands in the filled skutterudites
Hisatomo Harima and Katsuhiko Takegahara 2003 J. Phys.: Condens. Matter 15 S2081
-
Development of a remanence measurement-based SQUID system with in-depth resolution for nanoparticle imaging
Song Ge et al 2009 Phys. Med. Biol. 54 N177
-
A neutron diffraction and Rietveld analysis of cooperative Li motion in beta-eucryptite
Asel Sartbaeva et al 2004 J. Phys.: Condens. Matter 16 5267
Users also read
What's this?- On the exact solution for smooth pulses of the defocusing nonlinear Schrödinger modulation equations prior to breaking
- Analytical blowup solutions to the pressureless Navier–Stokes–Poisson equations with density-dependent viscosity in RN
- Ab initio self-consistent laser theory and random lasers
Related review articles
What's this?- Using multiscale norms to quantify mixing and transport
- Discrete breathers in Bose–Einstein condensates
- Tibetan singing bowls