 0176 Th. Gallay (Paris XI) and C.E. Wayne (Boston University)
 Longtime asymptotics of the NavierStokes and
vorticity equations on $R^3$
(217K, Postscript)
Feb 24, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We use the vorticity formulation to study the longtime
behavior of solutions to the NavierStokes equation on
$R^3$. We assume that the initial vorticity is small and
decays algebraically at infinity. After introducing
selfsimilar variables, we compute the longtime asymptotics
of the rescaled vorticity equation up to second order. Each
term in the asymptotics is a selfsimilar divergencefree
vector field with Gaussian decay at infinity, and the
coefficients in the expansion can be determined by solving
a finite system of ordinary differential equations. As a
consequence of our results, we are able to characterize the
set of solutions for which the velocity field satisfies
$\(\cdot,t)\_{L^2} = o(t^{5/4})$ as $t \to +\infty$.
In particular, we show that these solutions lie on a smooth
invariant submanifold of codimension $11$ in our function space.
 Files:
0176.src(
desc ,
0176.uu )