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Communications in Mathematical Physics

, Volume 273, Issue 3, pp 785–801 | Cite as

Partial Regularity of Solutions to the Four-Dimensional Navier-Stokes Equations at the First Blow-up Time

  • Hongjie DongEmail author
  • Dapeng Du
Article

Abstract

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.

Keywords

Weak Solution Heat Kernel Hausdorff Dimension Hausdorff Measure Energy Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  3. 3.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China

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