学术报告（申仲伟 2024.5.23）

摘要：This talk is concerned with the study of resolvent estimates in $L^p$ for the Stokes operator. Such estimates play an essential role in the functional analytic approach of Fujita and Kato to the nonlinear Navier-Stokes equations in bounded domains. In the case of smooth domains ($C^2$), the resolvent estimate is well known and holds for all $1<p<\infty$. If the domain is Lipschitz, the estimate was established for a limited range of p, depending on the dimension, using the method of layer potentials and a real-variable argument. In this talk, I will discuss some recent work, joint with Jun Geng, for the case of $ C^1$  domains. Starting with the upper half-space, using a perturbation argument, we are able to show that the resolvent estimate holds for all $1<p<\infty$. The case of exterior $ C^1$ domains is also studied.