报告题目: Emergent dynamics of infinitely many Cucker-Smale ensembles

报告人：王新宇（哈尔滨工业大学）

邀请人&主持人：黄辉

报告时间与地点：9月11日 2.30 pm，色情文学 203

报告摘要:  We study the emergent dynamics of the infinitely many Cucker--Smale ensembles without assuming compactness assumptions on spatial and velocity supports. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment force can be zero, so that the previous approach based on the energy method does not provide a quantitative flocking estimate. To overcome this difficulty, we introduce a suitable decay ansatz for the one-particle distribution function and an effective domain by identifying a time-varying region in which the total mass outside of it decays to zero asymptotically. Using these ingredients, we show that weak flocking dynamics emerges asymptotically in the sense that the second moment for velocity fluctuations around the velocity average tends to zero, whereas the second moment for spatial fluctuations around the center of mass remains uniformly bounded in time. Our results demonstrate the robustness of the emergent dynamics in the RKCS model across various non-compact, physically important distributions, including Gaussian distributions, sub-Gaussian distributions, and those with a finite D-th moment.

报告人介绍：王新宇，哈尔滨工业大学副研究员，主持国家自然科学基金青年学生基础研究项目（博士生研究生）和国家自然科学基金青年科学基金项目（C类）各一项，参与国自然基金3项。发表高质量论文多篇, 包括《Proc. Lond. Math. Soc.》、《Math. Ann.》、《J. Lond. Math. Soc.》、《SIAM J. Math. Anal.》、《Math. Models Methods Appl. Sci.》、《SIAM J. Appl. Dyn. Syst.》、《Nonlinearity》等。