Spatial C¹, C², and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients

2024/12/28 by Hongjie Dong, Dong, Hongjie, Hyunwoo Kwon +1
Mathematics · Computer Science · #Navier-Stokes equation solutions #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.20125

Abstract

We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having L₂-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.

Related

• Interior and boundary mixed norm derivative estimates for nonstationary Stokes equations
• Gradient estimates for Stokes systems with Dini mean oscillation coefficients
• Gradient estimates for Stokes systems in domains
• Gradient estimates for Stokes and Navier-Stokes systems with piecewise DMO coefficients
• Nonlocal Stokes equation with relaxation on the divergence free equation