Analyticity up to the boundary for the Prandtl and Navier-Stokes equations
数学专题报告
报告题目(Title)：Analyticity up to the boundary for the Prandtl and Navier-Stokes equations
报告人(Speaker)：李维喜 教授（武汉大学）
地点(Place)：后主楼1124
时间(Time)：2025年6月23日下午4:00-5:00
邀请人(Inviter)：许孝精
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.
