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M. Oliver and E.S. Titi,
Remark on the rate of decay of higher order derivatives
for solutions to the Navier-Stokes equations in
Rn,
J. Funct. Anal. 172 (2000), 1-18.
Abstract:
We present a new derivation of upper bounds for the decay of higher
order derivatives of solutions to the unforced Navier-Stokes equations
in Rn. The method, based on so-called Gevrey
estimates, also yields explicit bounds on the growth of the radius of
analyticity of the solution in time. Moreover, under the assumption
that the Navier-Stokes solution stays sufficiently close to a solution
of the heat equation in the L2 norm - a result known
to be true for a large class of initial data - lower bounds on the
decay of higher order derivatives can be obtained.
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