Analysis & PDE
- Anal. PDE
- Volume 2, Number 3 (2009), 361-366.
Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equation
Let . We consider the global Cauchy problem for the generalized Navier–Stokes system
for and , where is smooth and divergence free, and is a Fourier multiplier whose symbol is nonnegative; the case is essentially Navier–Stokes. It is folklore that one has global regularity in the critical and subcritical hyperdissipation regimes for . We improve this slightly by establishing global regularity under the slightly weaker condition that for all sufficiently large and some nondecreasing function such that . In particular, the results apply for the logarithmically supercritical dissipation .
Anal. PDE, Volume 2, Number 3 (2009), 361-366.
Received: 16 June 2009
Revised: 22 September 2009
Accepted: 23 October 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Tao, Terence. Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equation. Anal. PDE 2 (2009), no. 3, 361--366. doi:10.2140/apde.2009.2.361. https://projecteuclid.org/euclid.apde/1513798040