Dec. 3. 2024, Hyunwoo Kwon, Local $C^1$, $C^2$, and Schauder estimates for Stokes equations with variable coefficients II
Hyunwoo Kwon will give a talk at 12/03/2024.
I will present the joint work with Hongjie Dong on nonstationary Stokes equations with variable coefficients. In the second lecture, I will discuss the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form when the viscosity coefficients have $L_2$-Dini mean oscillations. As a corollary, I will present local Schauder estimates for such equations if the viscosity coefficient is $C^\alpha_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form.
Our result is sharp based on the well-known Serrin’s example.