Speaker: Prof. Fa Peng (Beihang University)

Title: The $L^p$ Neumann problem for the Stokes system in nonsmooth domains

Time: 10:00-11:00 August 21, 2026 (Friday)

Inviter: Prof. Jinping Zhuge (MCM, CAS)

Place: MCM110

Abstract: We are concerned with the solvability of the $L^p$ Neumann problem for the Stokes system on Lipschitz domains. By introducing a nonlinear weighted gradient, we establish global second-order estimates, improve reverse H\"older inequalities, and extend the solvability range for convex domains ($n\ge 3$). The method also covers semi-convex domains. For general Lipschitz domains, we prove solvability under a smallness condition on the second fundamental form in weak Lorentz spaces, covering all $W^{2,q}$ domains with $q>n-1$. This is joint work with Qianyun Miao.