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arXiv · 2412.20125

Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients

Hongjie Dong·Hyunwoo Kwon
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Abstract

We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for such equations if the viscosity coefficient belongs to $C^α_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form.

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Hongjie Dong, Hyunwoo Kwon. 2025-11-24. Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients. https://arxiv.org/abs/2412.20125

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