AI 中文总结
研究二维有界区域中由非局部、非线性乘性噪声驱动的抛物-抛物型Keller-Segel系统，通过引入定制截断系统、构建最大局部强解、引入特殊Lyapunov泛函等方法，建立了任意初始数据的强解的全局存在性和路径唯一性。
AI 中文摘要
本文研究二维有界区域中由非局部、非线性乘性噪声驱动的抛物-抛物型Keller-Segel系统。在适当假设下，建立了任意初始数据的强解的全局存在性和路径唯一性，无需任何小性条件，这与确定性二维Keller-Segel系统形成鲜明对比。主要分析挑战源于完全抛物耦合，以及趋化漂移和噪声项缺乏强制性和全局Lipschitz连续性。通过引入定制截断系统、构建最大局部强解、引入特殊Lyapunov泛函等步骤来克服这些问题。
英文摘要
In this paper, we study a stochastic parabolic-parabolic Keller-Segel system driven by nonlocal, nonlinear multiplicative noise in a two-dimensional bounded domain. Under suitable assumptions, we establish global existence and pathwise uniqueness of a strong solution for arbitrary initial data, without imposing any smallness conditions. This sharply contrasts with the deterministic two-dimensional Keller-Segel system, which typically requires smallness assumptions on initial mass. The main analytical challenges stem from the fully parabolic coupling, combined with a lack of coercivity and global Lipschitz continuity in both the chemotactic drift and noise terms. To overcome this, we introduce a tailored truncated system to establish local existence via Banach's fixed point theorem. Using this local existence and pathwise uniqueness, we construct a maximal local strong solution. Finally, by introducing a specialized Lyapunov functional, we derive uniform estimates to extend this solution globally.
