A note on the blow-up of solutions to the two-dimensional Keller-Segel model with tensorial flux

In the past decade, there has been much interest in analyzing Keller-Segel models with tensorial flux. However, it is yet not well understood whether there are solutions that blow-up in a finite amount of time. We aim to prove the possibility of having solutions blowing up in finite time when having a tensorial flux of the form A∇v, where A represents an arbitrary matrix with constant components satisfying Tr(A),det(A)>0.