Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 163, pp. 125.
Sharp asymptotic estimates for vorticity
solutions of the 2D NavierStokes equation
Yuncheng You
Abstract:
The asymptotic dynamics of highorder temporalspatial derivatives
of the twodimensional vorticity and velocity of an
incompressible, viscous fluid flow in
are studied,
which is equivalent to the 2D NavierStokes equation. It is known
that for any integrable initial vorticity, the 2D vorticity
solution converges to the Oseen vortex. In this paper, sharp
exterior decay estimates of the temporalspatial derivatives of
the vorticity solution are established. These estimates are then
used and combined with similarity and
compactness to show
the asymptotical attraction rates of temporalspatial derivatives
of generic 2D vorticity and velocity solutions by the Oseen
vortices and velocity solutions respectively. The asymptotic estimates
and the asymptotic attraction rates of all the derivatives obtained
in this paper are independent of low or high Reynolds numbers.
Submitted November 5, 2008. Published December 18, 2008.
Math Subject Classifications: 35B40, 35B65, 35K15, 35Q30, 76D05, 76D17.
Key Words: NavierStokes equation; vorticity; regularity; asymptotic dynamics;
BiotSavart law; similarity solution; Oseen vortex.
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Yuncheng You
Department of Mathematics and Statistics
University of South Florida
Tampa, FL 33620, USA
email: you@math.usf.edu

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