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


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.


Weak Solution Heat Kernel Hausdorff Dimension Hausdorff Measure Energy Inequality 
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© 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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