We are concerned with the dynamics of one-fold symmetric patches for the
two-dimensional aggregation equation associated to the Newtonian potential.
We reformulate a suitable graph model and prove a local well-posedness
result in subcritical and critical spaces. The global existence is obtained
only for small initial data using a weak damping property hidden in the
velocity terms. This allows us to analyze the concentration phenomenon of the
aggregation patches near the blow-up time. In particular, we prove that the patch
collapses to a collection of disjoint segments and we provide a description of the
singular measure through a careful study of the asymptotic behavior of the
graph.
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