报告题目：Analyticity up to the boundary for the Prandtl and Navier-Stokes equations
报 告 人：李维喜
工作单位：武汉大学
报告时间：2025年5月9日 15:00-18:00
会议地点：数信学院 305
报告摘要：We study the two-dimensional and three-dimensional Prandtl and Navier-Stokes equations in the half-space, and obtain the space-time analyticity of solutions to these equations. The analyticity estimates are local in time variable and global in space variable up to the boundary, with the lower bound of analyticity radii agreeing with that for the classical heat equation. The space-time analytic smoothing effect holds true for the Navier-Stokes equations with finite Sobolev regular initial data, and for the Prandtl equations with initial data real-analytic in tangential direction. The proof is based on direct energy estimate.
报告人简介：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.
