| Abstract: |
| The two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than 8pi and a finite second moment. Several constructive examples of such solutions have been obtained, where for all of them a perturbed stationary state undergoes scale instability and collapses at a point, resulting in a 8pi-mass concentration. It was conjectured that singular solutions concentrating simultaneously more than one solitons could exist. We construct rigorously such a new blowup mechanism, where two stationary states are simultaneously collapsing and colliding, resulting in a 16pi-mass concentration at a single blowup point, and with a new blowup rate which corresponds to the formal prediction by Seki, Sugiyama and Velazquez. We develop for the first time a robust framework to construct rigorously such blowup solutions involving simultaneously the non-radial collision and concentration of several solitons, which we expect to find applications to other evolution problems. |
|