In this paper, we obtain the sharp estimate on the asymptotic behaviors of blow-up profiles for Keller–Segel–Patlak system in the space with dimensions \(N\ge 3\) : 0.1 \(\begin{aligned} \left\{ \begin{array}{ll} u_t = \Delta u - \nabla \cdot (u\nabla v), & x\in \mathbb {R}^N, \ t\in (0,T), \\ 0 = \Delta v+u, & x\in \mathbb {R}^N, \ t\in (0,T), \\ u(x,0)=u_0(x), & x\in \mathbb {R}^N, \end{array} \right. \end{aligned}\) which solves an open problem proposed by Souplet and Winkler in [41]. 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.
