Hongjie Dong, Hyunwoo Kwon
Published 2023-08-18Version 1
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.
Nonstationary Stokes equations on a domain with curved boundary under slip boundary conditions
Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients
Maximum modulus estimate for the solution of the nonstationary Stokes equations
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