Finite-time Blow-up in a 2d Keller-Segel System with Rotation

In this talk we consider Neumann problem for 2D Keller-Segel system with rotation where the rotation angel is A. We prove that: In a general bounded domain, if the initial mass is large than 8π/cos(A), then there exists nonnegative initial datum such that the corresponding nonradial solution blows up in finite time and the blow-up point lies in the domain; if the boundary of the domain contains a line segment and the initial mass is large than 4π/cos(A)，then there exists nonnegative initial datum such that the nonradial solution blows up in finite time and the blow-up point lies in the line segment. Let the domain be a disc, if the initial mass is smaller than 8π/cos(A), then the radial solution exists globally in time; if the initial mass is smaller than 4π/cos(A), then the radial solution is globally bounded.

 李玉祥_学术报告海报20211008.pdf