报告题目 (Title)： Two-dimensional signal-dependent parabolic-elliptic Keller-Segel system and its mean field derivation (四)（二维奇性依赖的抛物-椭圆型的Keller-Segel方程和其平均场极限推导）
报告人 (Speaker)： Lukas Bol 博士（曼海姆大学）
报告时间 (Time)：2025年11月4日（周二）14:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：盛万成
报告摘要：We finish the discussion of the convergence of the particle trajectories. Under a regularity assumption of the initial data, we can use the relative entropy method to derive the strong L^1 convergence for the propagation of chaos, at least for short times. These restrictions are due to the term \nabla\log u^{\varepsilon}, which requires a uniform L^{\infty} bound in time and space. Therefor we introduce an equation for p=\nabla\log u^{\varepsilon}. The regularity assumption of the initial data allows us to infer uniform bounds on higher derivatives of u^{\varepsilon} and v^{\varepsilon} which appear as coefficients in the equation for p. Now the uniform bound for \nabla\log u^{\varepsilon} can be shown by a fix-point argument.