Geometric & Functional Analysis GAFA

, Volume 12, Issue 2, pp 355–379 | Cite as

A cheap Caffarelli—Kohn—Nirenberg inequality for the Navier—Stokes equation with hyper-dissipation

  • N.H. Katz
  • N. Pavlović

Abstract.

We prove that for the Navier—Stokes equation with dissipation \( (-\Delta)^\alpha \) where 1 < α < 5 /4, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most 5 — 4α. This unifies two directions from which one might approach the problem of global solvability, though it provides no direct progress on either.

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • N.H. Katz
    • 1
  • N. Pavlović
    • 2
  1. 1.Department of Mathematics, Washington University, St. Louis 63130, USA, e-mail: nets@math.wustl.eduUS
  2. 2.Department of Mathematics, Statistics, and Computer Science, Chicago Il 60607-7045, USA, e-mail: natasa@math.uic.eduUS

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