A cheap Caffarelli—Kohn—Nirenberg inequality for the Navier—Stokes equation with hyper-dissipation
- Cite this article as:
- Katz, N. & Pavlović, N. GAFA, Geom. funct. anal. (2002) 12: 355. doi:10.1007/s00039-002-8250-z
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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.