| Abstract: |
| In this talk, we consider the Keller-Segel-Patlak system in the whole space with dimensions $N\ge 3$. In the first part, we solves an open problem proposed by Souplet and Winkler in [CMP,2019]. To establish this result, we develop the zero number argument for nonlinear equations with unbounded coefficients and construct a family of auxiliary backward self-similar solutions through nontrivial ODE analysis. Examining the behavior of a parameter-dependent solution in the second part, we show the existence of a sharp threshold between extinction (i.e., convergence to 0) and blowup (i.e., convergence to \infty). This a joint work with Hai-Yang Jin, Jingyu Li and Maolin Zhou. |
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