 04186 Isabelle Gallagher, Thierry Gallay
 Uniqueness for the twodimensional NavierStokes equation with a
measure as initial vorticity
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Jun 15, 04

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Abstract. We show that any solution of the twodimensional NavierStokes
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
wellposed in the space of finite measures. In particular, this
provides an example of a situation where the NavierStokes equation is
wellposed for arbitrary data in a function space that is large enough
to contain the initial data of some selfsimilar solutions.
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