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{\it Finite-time blow-up of solutions of an aggregation equation}

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{\bf Thomas Laurent}\\
UCLA\\
{\tt laurent@math.ucla.edu}
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\noindent {\bf Abstract}:  The aggregation equation $u_t + div(u grad G * u  )
= 0$ arises in a number of contexts of recent interest in the physics and
biology literature. Depending on how regular the potential $G$ is, we prove
either local or global existence for the solutions. For example, we will see
that for $G(x)=exp(-|x|)$ we have local existence whereas for
$G(x)=exp(-|x|^2)$ we have global existence. For potential with a Lipschitz
point at the origin, e.g. $G(x)=exp(-|x|)$, we prove finite-time blow-up of
solutions from specific smooth initial data. 
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