Interior and boundary mixed norm derivative estimates for nonstationary Stokes equations

2023/08/18 by Hongjie Dong, Dong, Hongjie, Hyunwoo Kwon +1
Computer Science · Mathematics · #35B45 #35K51 #76D03 #76D07 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.09220

openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We obtain weighted mixed norm Sobolev estimates in the whole space for nonstationary Stokes equations in divergence and nondivergence form with variable viscosity coefficients that are merely measurable in time variable and have small mean oscillation in spatial variables in small cylinders. As an application, we prove interior mixed norm derivative estimates for solutions to both equations. We also discuss boundary mixed norm Hessian estimates for solutions to equations in nondivergence form under the Lions boundary conditions.

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