京师数学前沿论坛 第四十讲
京师数学前沿论坛
报告题目(Title)：Local well-posedness for the Boltzmann equation with hard potentials
报告人(Speaker)：李维喜 教授
地点(Place)：后主楼1124
时间(Time)：2026年6月29日上午10：00-11：00
报告摘要
We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and uniqueness of weak solutions, conditional to pointwise bounds on the hydrodynamic quantities (mass, energy, and entropy). Compared to the soft potential case, the key challenge for full-range hard potentials lies in the more severe loss of velocity moments. The proof combines a hypoelliptic estimate with interpolation inequalities to handle the moment-loss terms.
主讲人简介
李维喜，武汉大学数学与统计学院教授、博士生导师，国家杰出青年科学基金获得者，研究方向为微局部分析及其应用，主要从事流体力学方程的边界层理论，退化椭圆方程的正则性，以及谱分析等方面的研究，成果发表在Communications on Pure and Applied Mathematics、Journal of the European Mathematical Society、Advances in Mathematics等国际著名数学期刊上。曾主持国家优秀青年基金、霍英东教育基金、国际(地区)合作与交流项目等国家基金项目。目前担任KRM，DCDS-B，JPDE，CMAA等杂志编委。
