Isabelle Gallagher, Thierry Gallay
Uniqueness for the two-dimensional Navier-Stokes equation with a 
measure as initial vorticity
(474K, Postscript)

ABSTRACT.  We show that any solution of the two-dimensional Navier-Stokes 
equation whose vorticity distribution is uniformly bounded in 
$L^1(R^2)$ for positive times is entirely determined by the 
trace of the vorticity at $t = 0$, which is a finite measure. When 
combined with previous existence results by Cottet, by Giga, Miyakawa, 
and Osada, and by Kato, this uniqueness property implies that the 
Cauchy problem for the vorticity equation in $R^2$ is globally 
well-posed in the space of finite measures. In particular, this 
provides an example of a situation where the Navier-Stokes equation is 
well-posed for arbitrary data in a function space that is large enough 
to contain the initial data of some self-similar solutions.