| Abstract: |
| It is well known that the two-dimensional Keller-Segel system admits finite-time blow-up solutions when the initial density has total mass greater than (8\pi) and finite second moment. Several constructive examples of such solutions have been obtained, all exhibiting the same mechanism: a perturbed stationary state undergoes a scale instability and collapses at a point, leading to the concentration of a mass (8\pi).
It has long been conjectured that singular solutions involving the simultaneous concentration of more than one soliton could exist. In this work, we rigorously construct such a new blow-up mechanism. More precisely, we exhibit solutions in which two stationary states collapse simultaneously and collide, resulting in the concentration of a mass (16\pi) at a single blow-up point.
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